Browse Source

End presentation: finished

master
Joshua Moerman 11 years ago
parent
commit
c4412823c7
  1. 4
      make
  2. BIN
      presentation2/images/cat_contrafunctor.pdf
  3. 205
      presentation2/images/cat_contrafunctor.svg
  4. BIN
      presentation2/images/cat_functor.pdf
  5. 283
      presentation2/images/cat_functor.svg
  6. BIN
      presentation2/images/cat_th.pdf
  7. 215
      presentation2/images/cat_th.svg
  8. BIN
      presentation2/images/simplicial_abgrp.pdf
  9. 1260
      presentation2/images/simplicial_abgrp.svg
  10. 171
      presentation2/presentation.tex
  11. 6
      presentation2/symbols.tex

4
make

@ -13,8 +13,8 @@ Presentation2) pdflatex "../presentation2/presentation.tex" || exit 1
pdflatex "../presentation2/presentation.tex" || exit 1
mv presentation.pdf ../
;;
Symbols) pdflatex "../thesis/symbols.tex" || exit 1
pdflatex "../thesis/symbols.tex" || exit 1
Symbols) pdflatex "../presentation2/symbols.tex" || exit 1
pdflatex "../presentation2/symbols.tex" || exit 1
scp symbols.pdf moerman@stitch.science.ru.nl:~/symbols.pdf
ssh moerman@stitch.science.ru.nl 'pdf2svg symbols.pdf symbols.svg'
scp moerman@stitch.science.ru.nl:~/symbols.svg ../

BIN
presentation2/images/cat_contrafunctor.pdf

Binary file not shown.

205
presentation2/images/cat_contrafunctor.svg

@ -0,0 +1,205 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:cc="http://creativecommons.org/ns#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
width="319.10608"
height="72.310532"
id="svg4087"
version="1.1"
inkscape:version="0.48.2 r9819"
sodipodi:docname="cat_functor.svg">
<defs
id="defs4089" />
<sodipodi:namedview
id="base"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="2.0149341"
inkscape:cx="154.78853"
inkscape:cy="28.320563"
inkscape:document-units="px"
inkscape:current-layer="layer1"
showgrid="false"
fit-margin-left="1"
fit-margin-top="1"
fit-margin-bottom="1"
fit-margin-right="1"
inkscape:window-width="1280"
inkscape:window-height="752"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="0" />
<metadata
id="metadata4092">
<rdf:RDF>
<cc:Work
rdf:about="">
<dc:format>image/svg+xml</dc:format>
<dc:type
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
<dc:title></dc:title>
</cc:Work>
</rdf:RDF>
</metadata>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
transform="translate(-108.56303,-922.57636)">
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 122.41993,965.69537 5.0586,0 0.5664,3.63281 1.58204,0 -1.875,-12.44141 -1.5625,0 -7.16797,12.44141 1.32812,0 2.07031,-3.63281 z m 4.92188,-1.01563 -4.33594,0 1.95313,-3.45704 c 0.23437,-0.41015 1.36718,-2.48046 1.58203,-2.98827 l 0.0195,0 c -0.039,0.48827 0.13673,1.67969 0.19531,2.20702 l 0.58594,4.23829 z m 0,0"
id="path3616" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 174.65191,956.88676 -2.65625,12.44141 4.62892,0 c 2.8125,0 5.15625,-1.99219 5.15625,-3.86719 0,-1.26954 -1.11329,-2.36329 -2.8125,-2.63672 1.75781,-0.41015 3.55468,-1.62109 3.55468,-3.26172 0,-1.52343 -1.5625,-2.67578 -3.73047,-2.67578 l -4.14063,0 z m 0.29298,5.42968 0.95702,-4.43358 2.1875,0 c 1.73829,0 3.04688,0.78125 3.04688,1.875 0,1.23046 -1.77734,2.55858 -3.96484,2.55858 l -2.22656,0 z m -1.26954,6.01563 1.03516,-4.9414 2.40234,0 c 1.99219,0 3.22266,0.99609 3.22266,2.1875 0,1.44531 -1.875,2.7539 -3.98437,2.7539 l -2.67579,0 z m 0,0"
id="path3612" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 124.13214,935.44435 c 0,-0.15625 -0.13673,-0.21485 -0.21485,-0.21485 -0.42969,0 -0.9375,1.15235 -3.47657,1.15235 -3.14452,0 -4.04296,-1.9336 -4.04296,-4.60938 0,-2.67578 0.95703,-4.60937 3.90625,-4.60937 1.60156,0 2.4414,0.625 2.92969,1.01562 0.0976,0.0977 0.15625,0.15625 0.27344,0.15625 0.0781,0 0.17577,-0.0781 0.17577,-0.15625 l 0.3711,-1.99218 c 0.0195,-0.0781 0,-0.13672 -0.13672,-0.19532 -1.07422,-0.39062 -2.16797,-0.64453 -3.55469,-0.64453 -4.375,0 -6.62109,2.12891 -6.62109,6.40625 0,4.39453 2.28515,6.42578 6.64063,6.42578 1.52343,0 2.46093,-0.21484 3.76952,-1.01562 0.15625,-0.0977 0.11713,-0.21485 0.11713,-0.21485 l -0.13672,-1.5039 z m 0,0"
id="path3592" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 290.53539,923.57636 c -0.64454,0 -0.85937,0.19531 -0.85937,0.85937 l 0,10.72266 c 0,0.64453 0.19531,0.85937 0.85937,0.85937 l 4.72656,0 c 4.375,0 5.89844,-2.61719 5.89844,-6.13281 0,-1.40625 -0.23438,-3.16406 -1.23048,-4.43359 -1.34765,-1.66016 -3.49608,-1.875 -4.66796,-1.875 l -4.72656,0 z m 1.71875,10.89843 0,-9.35547 2.28515,0 c 3.88672,0 4.04297,2.75391 4.04297,4.76563 0,2.03125 -0.19531,4.58984 -4.02343,4.58984 l -2.30469,0 z m 0,0"
id="path3588" />
<g
id="g4299"
transform="translate(42.681296,-1.4888824)">
<path
id="path3620"
d="m 255.6779,960.34895 5.33204,0 0.23438,-1.07423 -5.33204,0 0.97656,-4.55077 2.30469,0 c 0.21485,0 0.42969,0.0195 0.64454,0.0195 l 3.10546,0 0.23437,-1.13282 -7.59765,0 -2.63672,12.40235 1.54297,0 1.1914,-5.66406 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3624"
d="m 268.46432,952.57551 c -2.69532,2.40234 -3.35938,6.03515 -3.35938,8.96484 0,3.14453 0.76171,6.66016 3.35938,8.96485 l 1.07421,0 c -0.70313,-0.64454 -1.79688,-2.03125 -2.42188,-4.0625 -0.46875,-1.60157 -0.66406,-3.26173 -0.66406,-4.90235 0,-5.27344 1.89454,-7.87109 3.08594,-8.96484 l -1.07421,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3628"
d="m 274.41415,962.3802 5.0586,0 0.5664,3.63281 1.58204,0 -1.875,-12.44141 -1.5625,0 -7.16798,12.44141 1.32813,0 2.07031,-3.63281 z m 4.92188,-1.01563 -4.33594,0 1.95312,-3.45704 c 0.23438,-0.41015 1.36719,-2.48046 1.58204,-2.98827 l 0.0195,0 c -0.039,0.48827 0.13673,1.67969 0.19531,2.20702 l 0.58594,4.23829 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3632"
d="m 284.18071,970.5052 c 2.67579,-2.40235 3.35938,-6.03517 3.35938,-8.96485 0,-3.14453 -0.76171,-6.66015 -3.35938,-8.96484 l -1.07421,0 c 0.68359,0.64452 1.77734,2.03125 2.42188,4.0625 0.46875,1.60156 0.64452,3.26171 0.64452,4.90234 0,5.27343 -1.875,7.8711 -3.0664,8.96485 l 1.07421,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<g
id="g4263"
transform="translate(54.592356,45.162766)">
<path
id="path3636"
d="m 322.24619,914.68989 5.33203,0 0.23438,-1.07423 -5.33204,0 0.97656,-4.55077 2.30469,0 c 0.21485,0 0.42969,0.0195 0.64454,0.0195 l 3.10546,0 0.23438,-1.13282 -7.59765,0 -2.63673,12.40235 1.54298,0 1.1914,-5.66406 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3640"
d="m 335.03261,906.91645 c -2.69531,2.40234 -3.35937,6.03515 -3.35937,8.96484 0,3.14453 0.76171,6.66016 3.35937,8.96485 l 1.07421,0 c -0.70312,-0.64454 -1.79687,-2.03125 -2.42187,-4.0625 -0.46875,-1.60157 -0.66406,-3.26173 -0.66406,-4.90235 0,-5.27344 1.89453,-7.87109 3.08593,-8.96484 l -1.07421,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3644"
d="m 341.41212,907.91254 -2.65625,12.44141 4.62892,0 c 2.8125,0 5.15625,-1.99219 5.15625,-3.86719 0,-1.26954 -1.11329,-2.36329 -2.8125,-2.63672 1.75781,-0.41015 3.55468,-1.62109 3.55468,-3.26172 0,-1.52343 -1.5625,-2.67578 -3.73047,-2.67578 l -4.14063,0 z m 0.29298,5.42968 0.95702,-4.43358 2.1875,0 c 1.73829,0 3.04688,0.78125 3.04688,1.875 0,1.23046 -1.77734,2.55858 -3.96484,2.55858 l -2.22656,0 z m -1.26954,6.01563 1.03516,-4.9414 2.40234,0 c 1.99219,0 3.22266,0.99609 3.22266,2.1875 0,1.44531 -1.875,2.7539 -3.98437,2.7539 l -2.67579,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3648"
d="m 352.29775,924.84614 c 2.67578,-2.40235 3.35937,-6.03517 3.35937,-8.96485 0,-3.14453 -0.76171,-6.66015 -3.35937,-8.96484 l -1.07422,0 c 0.68359,0.64452 1.77734,2.03125 2.42188,4.0625 0.46875,1.60156 0.64452,3.26171 0.64452,4.90234 0,5.27343 -1.875,7.8711 -3.0664,8.96485 l 1.07422,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<g
id="g4331"
transform="translate(-6.948118,7.9407064)">
<path
id="path3688"
d="m 350.68838,964.01833 4.43358,0 0.19532,-0.89843 -4.43359,0 0.80077,-3.78907 1.9336,0 c 0.17578,0 0.35157,0.0195 0.52734,0.0195 l 2.59766,0 0.19532,-0.9375 -6.34767,0 -2.1875,10.33204 1.28907,0 0.9961,-4.72656 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3692"
d="m 359.33414,957.53396 c -2.22656,2.01171 -2.79296,5.03906 -2.79296,7.48046 0,2.61719 0.64452,5.54687 2.79296,7.48047 l 0.89844,0 c -0.5664,-0.54687 -1.48438,-1.69922 -2.01172,-3.39843 -0.41016,-1.32813 -0.54687,-2.71485 -0.54687,-4.0625 0,-4.41406 1.5625,-6.5625 2.55859,-7.5 l -0.89844,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3696"
d="m 363.8679,962.98317 1.60156,0 0.17579,-0.8789 -1.6211,0 0.39063,-1.83594 c 0.23437,-1.03516 1.25,-1.15235 1.58203,-1.15235 0.27344,0 0.68359,0.0586 1.11328,0.25392 l 0.21485,-0.9961 c -0.0781,-0.0195 -0.54688,-0.15625 -1.13282,-0.15625 -1.40624,0 -2.63672,1.11328 -2.92968,2.48047 l -0.3125,1.40625 -1.09375,0 -0.17579,0.8789 1.07423,0 -1.21094,5.76172 1.09375,0 1.23046,-5.76172 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3700"
d="m 369.45227,972.49489 c 2.2461,-1.99218 2.8125,-5.03906 2.8125,-7.46093 0,-2.63673 -0.64452,-5.56641 -2.8125,-7.5 l -0.89843,0 c 0.58593,0.54687 1.50391,1.69921 2.03125,3.39844 0.39062,1.32812 0.54687,2.71483 0.54687,4.08202 0,4.39454 -1.5625,6.5625 -2.57812,7.48047 l 0.89843,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 149.00363,972.41275 1.60156,0 0.17578,-0.8789 -1.62109,0 0.39062,-1.83594 c 0.23438,-1.03516 1.25,-1.15235 1.58204,-1.15235 0.27343,0 0.68358,0.0586 1.11327,0.25392 l 0.21485,-0.9961 c -0.0781,-0.0195 -0.54687,-0.15625 -1.13281,-0.15625 -1.40625,0 -2.63672,1.11328 -2.92969,2.48047 l -0.3125,1.40625 -1.09375,0 -0.17578,0.8789 1.07422,0 -1.21094,5.76173 1.09375,0 1.23047,-5.76173 z m 0,0"
id="path3676" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 236.33466,944.70721 5.33204,0 0.23438,-1.07423 -5.33204,0 0.97656,-4.55077 2.30469,0 c 0.21485,0 0.42969,0.0195 0.64454,0.0195 l 3.10546,0 0.23437,-1.13282 -7.59765,0 -2.63672,12.40235 1.54297,0 1.1914,-5.66406 z m 0,0"
id="path3620-4" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 204.47319,963.02924 c 18.55162,-6.79809 56.78174,1.45336 67.9923,-0.4963"
id="path4323"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 263.0359,956.08112 c 20.67726,4.1454 0.23648,12.24432 -3.47406,14.39253"
id="path4325"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 148.07256,940.41659 c -15.50872,-4.53937 -41.01787,7.49912 -37.71836,27.29618 2.8815,17.28897 12.7589,21.37971 30.27395,23.32583 102.12055,11.3467 53.7195,-90.50263 -9.92589,-49.13313"
id="path4404"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 325.74586,939.9203 c -14.76394,-3.21924 -44.49933,3.45869 -46.65165,22.82953 -2.10589,18.95304 14.85107,25.53317 30.27394,27.29618 200.99908,22.97649 102.0719,-81.0735 3.47406,-53.59977"
id="path4406"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cssc" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 109.18471,56.766023 c 10.01896,-0.04259 26.54973,0.754697 32.25912,0.992588"
id="path4408"
inkscape:connector-curvature="0"
transform="translate(24.495316,906.4801)" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 137.96977,52.79567 c 13.79724,5.124392 -1.26977,6.772129 -1.48888,7.940706"
id="path4410"
inkscape:connector-curvature="0"
transform="translate(24.495316,906.4801)" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 368.42716,958.28318 c -10.05621,1.66948 -24.79489,0.85814 -32.75542,0.4963"
id="path4414"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 340.13839,954.31283 c -12.72793,5.67089 -8.06753,6.18887 0.99259,11.91106"
id="path4416"
inkscape:connector-curvature="0" />
</g>
</svg>

After

Width:  |  Height:  |  Size: 13 KiB

BIN
presentation2/images/cat_functor.pdf

Binary file not shown.

283
presentation2/images/cat_functor.svg

@ -0,0 +1,283 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:cc="http://creativecommons.org/ns#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
width="411.06058"
height="92.49913"
id="svg4087"
version="1.1"
inkscape:version="0.48.2 r9819"
sodipodi:docname="cat_functor.svg">
<defs
id="defs4089" />
<sodipodi:namedview
id="base"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="2.0149341"
inkscape:cx="216.02672"
inkscape:cy="37.375838"
inkscape:document-units="px"
inkscape:current-layer="layer1"
showgrid="false"
fit-margin-left="1"
fit-margin-top="1"
fit-margin-bottom="1"
fit-margin-right="1"
inkscape:window-width="1280"
inkscape:window-height="752"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="0" />
<metadata
id="metadata4092">
<rdf:RDF>
<cc:Work
rdf:about="">
<dc:format>image/svg+xml</dc:format>
<dc:type
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
<dc:title />
</cc:Work>
</rdf:RDF>
</metadata>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
transform="translate(-47.324847,-911.44304)">
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 66.834986,965.19906 5.0586,0 0.5664,3.63281 1.58204,0 -1.875,-12.44141 -1.5625,0 -7.16797,12.44141 1.32812,0 2.07031,-3.63281 z m 4.92188,-1.01563 -4.33594,0 1.95313,-3.45704 c 0.23437,-0.41015 1.36718,-2.48046 1.58203,-2.98827 l 0.0195,0 c -0.039,0.48827 0.13673,1.67969 0.19531,2.20702 l 0.58594,4.23829 z m 0,0"
id="path3616" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 126.01509,941.50164 -2.65625,12.44141 4.62892,0 c 2.8125,0 5.15625,-1.99219 5.15625,-3.86719 0,-1.26954 -1.11329,-2.36329 -2.8125,-2.63672 1.75781,-0.41015 3.55468,-1.62109 3.55468,-3.26172 0,-1.52343 -1.5625,-2.67578 -3.73047,-2.67578 l -4.14063,0 z m 0.29298,5.42968 0.95702,-4.43358 2.1875,0 c 1.73829,0 3.04688,0.78125 3.04688,1.875 0,1.23046 -1.77734,2.55858 -3.96484,2.55858 l -2.22656,0 z m -1.26954,6.01563 1.03516,-4.9414 2.40234,0 c 1.99219,0 3.22266,0.99609 3.22266,2.1875 0,1.44531 -1.875,2.7539 -3.98437,2.7539 l -2.67579,0 z m 0,0"
id="path3612" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 184.26318,959.2821 c -1.17188,-0.48829 -2.10938,-0.625 -3.16406,-0.625 -3.96485,0 -7.20704,4.17969 -7.20704,7.94921 0,2.75391 1.83594,4.86329 4.29687,4.86329 1.9336,0 2.63673,-0.19532 3.86719,-0.97656 l 0.15625,-1.25 c -1.21094,0.80077 -1.97265,1.11327 -3.49609,1.11327 -2.22656,0 -3.26172,-1.83594 -3.26172,-3.86719 0,-3.10546 2.42187,-6.69921 5.44922,-6.69921 1.21094,0 1.95313,0.3125 2.79297,0.95703 l 0.56641,-1.46484 z m 0,0"
id="path3608" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 68.547201,922.5407 c 0,-0.15625 -0.13673,-0.21485 -0.21485,-0.21485 -0.42969,0 -0.9375,1.15235 -3.47657,1.15235 -3.14452,0 -4.04296,-1.9336 -4.04296,-4.60938 0,-2.67578 0.95703,-4.60937 3.90625,-4.60937 1.60156,0 2.4414,0.625 2.92969,1.01562 0.0976,0.0977 0.15625,0.15625 0.27344,0.15625 0.0781,0 0.17577,-0.0781 0.17577,-0.15625 l 0.3711,-1.99218 c 0.0195,-0.0781 0,-0.13672 -0.13672,-0.19532 -1.07422,-0.39062 -2.16797,-0.64453 -3.55469,-0.64453 -4.375,0 -6.62109,2.12891 -6.62109,6.40625 0,4.39453 2.28515,6.42578 6.64063,6.42578 1.52343,0 2.46093,-0.21484 3.76952,-1.01562 0.15625,-0.0977 0.11713,-0.21485 0.11713,-0.21485 l -0.13672,-1.5039 z m 0,0"
id="path3592" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 284.57987,913.15419 c -0.64454,0 -0.85937,0.19531 -0.85937,0.85937 l 0,10.72266 c 0,0.64453 0.19531,0.85937 0.85937,0.85937 l 4.72656,0 c 4.375,0 5.89844,-2.61719 5.89844,-6.13281 0,-1.40625 -0.23438,-3.16406 -1.23048,-4.43359 -1.34765,-1.66016 -3.49608,-1.875 -4.66796,-1.875 l -4.72656,0 z m 1.71875,10.89843 0,-9.35547 2.28515,0 c 3.88672,0 4.04297,2.75391 4.04297,4.76563 0,2.03125 -0.19531,4.58984 -4.02343,4.58984 l -2.30469,0 z m 0,0"
id="path3588" />
<g
id="g4299"
transform="translate(33.251707,0.49629413)">
<path
id="path3620"
d="m 255.6779,960.34895 5.33204,0 0.23438,-1.07423 -5.33204,0 0.97656,-4.55077 2.30469,0 c 0.21485,0 0.42969,0.0195 0.64454,0.0195 l 3.10546,0 0.23437,-1.13282 -7.59765,0 -2.63672,12.40235 1.54297,0 1.1914,-5.66406 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3624"
d="m 268.46432,952.57551 c -2.69532,2.40234 -3.35938,6.03515 -3.35938,8.96484 0,3.14453 0.76171,6.66016 3.35938,8.96485 l 1.07421,0 c -0.70313,-0.64454 -1.79688,-2.03125 -2.42188,-4.0625 -0.46875,-1.60157 -0.66406,-3.26173 -0.66406,-4.90235 0,-5.27344 1.89454,-7.87109 3.08594,-8.96484 l -1.07421,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3628"
d="m 274.41415,962.3802 5.0586,0 0.5664,3.63281 1.58204,0 -1.875,-12.44141 -1.5625,0 -7.16798,12.44141 1.32813,0 2.07031,-3.63281 z m 4.92188,-1.01563 -4.33594,0 1.95312,-3.45704 c 0.23438,-0.41015 1.36719,-2.48046 1.58204,-2.98827 l 0.0195,0 c -0.039,0.48827 0.13673,1.67969 0.19531,2.20702 l 0.58594,4.23829 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3632"
d="m 284.18071,970.5052 c 2.67579,-2.40235 3.35938,-6.03517 3.35938,-8.96485 0,-3.14453 -0.76171,-6.66015 -3.35938,-8.96484 l -1.07421,0 c 0.68359,0.64452 1.77734,2.03125 2.42188,4.0625 0.46875,1.60156 0.64452,3.26171 0.64452,4.90234 0,5.27343 -1.875,7.8711 -3.0664,8.96485 l 1.07421,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<g
id="g4263"
transform="translate(32.259119,21.340648)">
<path
id="path3636"
d="m 322.24619,914.68989 5.33203,0 0.23438,-1.07423 -5.33204,0 0.97656,-4.55077 2.30469,0 c 0.21485,0 0.42969,0.0195 0.64454,0.0195 l 3.10546,0 0.23438,-1.13282 -7.59765,0 -2.63673,12.40235 1.54298,0 1.1914,-5.66406 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3640"
d="m 335.03261,906.91645 c -2.69531,2.40234 -3.35937,6.03515 -3.35937,8.96484 0,3.14453 0.76171,6.66016 3.35937,8.96485 l 1.07421,0 c -0.70312,-0.64454 -1.79687,-2.03125 -2.42187,-4.0625 -0.46875,-1.60157 -0.66406,-3.26173 -0.66406,-4.90235 0,-5.27344 1.89453,-7.87109 3.08593,-8.96484 l -1.07421,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3644"
d="m 341.41212,907.91254 -2.65625,12.44141 4.62892,0 c 2.8125,0 5.15625,-1.99219 5.15625,-3.86719 0,-1.26954 -1.11329,-2.36329 -2.8125,-2.63672 1.75781,-0.41015 3.55468,-1.62109 3.55468,-3.26172 0,-1.52343 -1.5625,-2.67578 -3.73047,-2.67578 l -4.14063,0 z m 0.29298,5.42968 0.95702,-4.43358 2.1875,0 c 1.73829,0 3.04688,0.78125 3.04688,1.875 0,1.23046 -1.77734,2.55858 -3.96484,2.55858 l -2.22656,0 z m -1.26954,6.01563 1.03516,-4.9414 2.40234,0 c 1.99219,0 3.22266,0.99609 3.22266,2.1875 0,1.44531 -1.875,2.7539 -3.98437,2.7539 l -2.67579,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3648"
d="m 352.29775,924.84614 c 2.67578,-2.40235 3.35937,-6.03517 3.35937,-8.96485 0,-3.14453 -0.76171,-6.66015 -3.35937,-8.96484 l -1.07422,0 c 0.68359,0.64452 1.77734,2.03125 2.42188,4.0625 0.46875,1.60156 0.64452,3.26171 0.64452,4.90234 0,5.27343 -1.875,7.8711 -3.0664,8.96485 l 1.07422,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<g
id="g3768"
transform="matrix(1.2499999,0,0,1.2499999,162.86603,807.98783)">
<path
id="path3652"
d="m 199.86537,131.41776 4.26563,0 0.1875,-0.85938 -4.26563,0 0.78125,-3.64062 1.84375,0 c 0.17188,0 0.34375,0.0156 0.51563,0.0156 l 2.48437,0 0.1875,-0.90625 -6.07812,0 -2.10938,9.92188 1.23438,0 0.95312,-4.53125 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3656"
d="m 210.0945,125.19901 c -2.15625,1.92187 -2.6875,4.82812 -2.6875,7.17187 0,2.51563 0.60937,5.32813 2.6875,7.17188 l 0.85937,0 c -0.5625,-0.51563 -1.4375,-1.625 -1.9375,-3.25 -0.375,-1.28125 -0.53125,-2.60938 -0.53125,-3.92188 0,-4.21875 1.51563,-6.29687 2.46875,-7.17187 l -0.85937,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3660"
d="m 221.90125,126.32401 c -0.9375,-0.39063 -1.6875,-0.5 -2.53125,-0.5 -3.17188,0 -5.76563,3.34375 -5.76563,6.35937 0,2.20313 1.46875,3.89063 3.4375,3.89063 1.54688,0 2.10938,-0.15625 3.09375,-0.78125 l 0.125,-1 c -0.96875,0.64062 -1.57812,0.89062 -2.79687,0.89062 -1.78125,0 -2.60938,-1.46875 -2.60938,-3.09375 0,-2.48437 1.9375,-5.35937 4.35938,-5.35937 0.96875,0 1.5625,0.25 2.23437,0.76562 l 0.45313,-1.17187 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3664"
d="m 224.08763,139.54276 c 2.14063,-1.92188 2.6875,-4.82813 2.6875,-7.17188 0,-2.51562 -0.60937,-5.32812 -2.6875,-7.17187 l -0.85937,0 c 0.54687,0.51562 1.42187,1.625 1.9375,3.25 0.375,1.28125 0.51562,2.60937 0.51562,3.92187 0,4.21875 -1.5,6.29688 -2.45312,7.17188 l 0.85937,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<g
id="g4331"
transform="translate(-12.407354,-3.9703532)">
<path
id="path3688"
d="m 350.68838,964.01833 4.43358,0 0.19532,-0.89843 -4.43359,0 0.80077,-3.78907 1.9336,0 c 0.17578,0 0.35157,0.0195 0.52734,0.0195 l 2.59766,0 0.19532,-0.9375 -6.34767,0 -2.1875,10.33204 1.28907,0 0.9961,-4.72656 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3692"
d="m 359.33414,957.53396 c -2.22656,2.01171 -2.79296,5.03906 -2.79296,7.48046 0,2.61719 0.64452,5.54687 2.79296,7.48047 l 0.89844,0 c -0.5664,-0.54687 -1.48438,-1.69922 -2.01172,-3.39843 -0.41016,-1.32813 -0.54687,-2.71485 -0.54687,-4.0625 0,-4.41406 1.5625,-6.5625 2.55859,-7.5 l -0.89844,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3696"
d="m 363.8679,962.98317 1.60156,0 0.17579,-0.8789 -1.6211,0 0.39063,-1.83594 c 0.23437,-1.03516 1.25,-1.15235 1.58203,-1.15235 0.27344,0 0.68359,0.0586 1.11328,0.25392 l 0.21485,-0.9961 c -0.0781,-0.0195 -0.54688,-0.15625 -1.13282,-0.15625 -1.40624,0 -2.63672,1.11328 -2.92968,2.48047 l -0.3125,1.40625 -1.09375,0 -0.17579,0.8789 1.07423,0 -1.21094,5.76172 1.09375,0 1.23046,-5.76172 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3700"
d="m 369.45227,972.49489 c 2.2461,-1.99218 2.8125,-5.03906 2.8125,-7.46093 0,-2.63673 -0.64452,-5.56641 -2.8125,-7.5 l -0.89843,0 c 0.58593,0.54687 1.50391,1.69921 2.03125,3.39844 0.39062,1.32812 0.54687,2.71483 0.54687,4.08202 0,4.39454 -1.5625,6.5625 -2.57812,7.48047 l 0.89843,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<g
id="g4341"
transform="translate(-12.407354,-3.9703532)">
<path
id="path3704"
d="m 414.39428,949.1295 4.43359,0 0.19531,-0.89843 -4.43358,0 0.80077,-3.78907 1.9336,0 c 0.17578,0 0.35156,0.0195 0.52734,0.0195 l 2.59766,0 0.19531,-0.9375 -6.34766,0 -2.1875,10.33204 1.28906,0 0.9961,-4.72656 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3708"
d="m 423.04006,942.64513 c -2.22656,2.01171 -2.79296,5.03906 -2.79296,7.48046 0,2.61719 0.64452,5.54687 2.79296,7.48047 l 0.89844,0 c -0.5664,-0.54687 -1.48438,-1.69922 -2.01172,-3.39843 -0.41016,-1.32813 -0.54687,-2.71485 -0.54687,-4.0625 0,-4.41406 1.5625,-6.5625 2.55859,-7.5 l -0.89844,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3712"
d="m 432.14413,947.07872 c -0.54687,0 -1.34765,0.0586 -2.40233,0.46875 -0.29298,-0.27344 -0.76173,-0.46875 -1.28907,-0.46875 -1.50391,0 -2.91016,1.46485 -2.91016,2.92968 0,0.52735 0.23438,0.95704 0.23438,0.95704 -0.2539,0.2539 -0.74219,0.8789 -0.74219,1.66015 0,0.44922 0.15625,0.72266 0.17579,0.76172 -0.95704,0.50782 -1.28907,1.30859 -1.28907,1.79688 0,0.91796 1.07422,1.73827 2.85157,1.73827 1.5625,0 3.71093,-0.76171 3.71093,-2.46093 0,-0.95703 -0.60547,-1.66015 -2.61718,-1.66015 l -1.26954,0 c -0.29296,0 -0.70313,0 -0.70313,-0.58594 0,-0.17579 0,-0.41016 0.29298,-0.74219 0.23437,0.19531 0.66406,0.42969 1.25,0.42969 1.48437,0 2.91015,-1.44531 2.91015,-2.92969 0,-0.54687 -0.2539,-0.97656 -0.2539,-0.9961 0.0586,0.039 0.0781,0.039 0.0976,0.039 0.0781,0 0.52735,-0.0586 1.15235,-0.0586 0.3125,0 0.42969,0 0.78125,0.0195 l 0.0195,-0.89844 z m -4.53125,4.00391 c -0.625,0 -1.03515,-0.3711 -1.03515,-1.09375 0,-0.87891 0.5664,-2.08985 1.69922,-2.08985 0.39062,0 1.03516,0.17579 1.03516,1.09375 0,0.9375 -0.58594,2.08985 -1.69923,2.08985 z m 0.0195,2.8125 c 0.99609,0 1.77734,0.19531 1.77734,0.8789 0,0.76172 -1.23046,1.32812 -2.46094,1.32812 -1.17187,0 -1.97265,-0.44921 -1.97265,-1.03515 0,-0.23437 0.21484,-1.17187 1.36719,-1.17187 l 1.28906,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3716"
d="m 434.39568,957.60606 c 2.2461,-1.99218 2.8125,-5.03906 2.8125,-7.46093 0,-2.63673 -0.64452,-5.56641 -2.8125,-7.5 l -0.89844,0 c 0.58594,0.54687 1.50392,1.69921 2.03125,3.39844 0.39063,1.32812 0.54688,2.71483 0.54688,4.08202 0,4.39454 -1.5625,6.5625 -2.57813,7.48047 l 0.89844,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 103.34458,963.47945 1.60156,0 0.17578,-0.8789 -1.62109,0 0.39062,-1.83594 c 0.23438,-1.03516 1.25,-1.15235 1.58204,-1.15235 0.27343,0 0.68358,0.0586 1.11327,0.25392 l 0.21485,-0.9961 c -0.0781,-0.0195 -0.54687,-0.15625 -1.13281,-0.15625 -1.40625,0 -2.63672,1.11328 -2.92969,2.48047 l -0.3125,1.40625 -1.09375,0 -0.17578,0.8789 1.07422,0 -1.21094,5.76173 1.09375,0 1.23047,-5.76173 z m 0,0"
id="path3676" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 162.51183,943.10836 c -0.54687,0 -1.34765,0.0586 -2.40233,0.46875 -0.29298,-0.27344 -0.76173,-0.46875 -1.28907,-0.46875 -1.50391,0 -2.91016,1.46485 -2.91016,2.92968 0,0.52735 0.23438,0.95704 0.23438,0.95704 -0.2539,0.2539 -0.74219,0.8789 -0.74219,1.66015 0,0.44923 0.15625,0.72266 0.17579,0.76173 -0.95704,0.50781 -1.28907,1.30858 -1.28907,1.79687 0,0.91796 1.07422,1.73828 2.85157,1.73828 1.5625,0 3.71093,-0.76172 3.71093,-2.46094 0,-0.95703 -0.60547,-1.66015 -2.61718,-1.66015 l -1.26954,0 c -0.29296,0 -0.70313,0 -0.70313,-0.58594 0,-0.17579 0,-0.41016 0.29298,-0.74219 0.23437,0.19532 0.66406,0.42969 1.25,0.42969 1.48437,0 2.91015,-1.44531 2.91015,-2.92969 0,-0.54687 -0.2539,-0.97656 -0.2539,-0.9961 0.0586,0.039 0.0781,0.039 0.0976,0.039 0.0781,0 0.52735,-0.0586 1.15235,-0.0586 0.3125,0 0.42969,0 0.78125,0.0195 l 0.0195,-0.89844 z m -4.53125,4.00391 c -0.625,0 -1.03515,-0.3711 -1.03515,-1.09375 0,-0.87891 0.5664,-2.08985 1.69922,-2.08985 0.39062,0 1.03516,0.17579 1.03516,1.09375 0,0.9375 -0.58594,2.08985 -1.69923,2.08985 z m 0.0195,2.8125 c 0.99609,0 1.77734,0.19531 1.77734,0.8789 0,0.76172 -1.23046,1.32812 -2.46094,1.32812 -1.17187,0 -1.97265,-0.44921 -1.97265,-1.03515 0,-0.23437 0.21484,-1.17187 1.36719,-1.17187 l 1.28906,0 z m 0,0"
id="path3672" />
<path
style="fill:none;stroke:#000000;stroke-width:0.83960366px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 123.652,925.78188 c -21.1044,-5.82735 -70.826164,8.10203 -74.639361,33.00039 -7.019973,45.83703 126.052321,55.65003 143.669981,17.30508 23.9816,-52.19613 -79.72057,-77.18962 -106.997464,-42.65904"
id="path4273"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:0.89016008px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 364.50379,919.40572 c -22.79839,-4.83377 -87.05111,7.42867 -83.17734,42.97505 6.58458,60.42123 236.51818,52.11463 160.06017,-21.70458 -14.79232,-14.28184 -29.08146,-22.13865 -50.80562,-22.13865 -19.15763,0 -34.04239,-4.46227 -52.15444,0.43409"
id="path4275"
inkscape:connector-curvature="0"
sodipodi:nodetypes="csssc" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 239.80872,948.18127 5.33204,0 0.23438,-1.07423 -5.33204,0 0.97656,-4.55077 2.30469,0 c 0.21485,0 0.42969,0.0195 0.64454,0.0195 l 3.10546,0 0.23437,-1.13282 -7.59765,0 -2.63672,12.40235 1.54297,0 1.1914,-5.66406 z m 0,0"
id="path3620-4" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 80.399651,962.53294 c 11.35166,0.79403 32.481519,-10.10269 35.236879,-11.41476"
id="path4307"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 110.67359,949.62929 c 15.26558,-0.8072 0.48302,6.76229 0.49629,6.94812"
id="path4309"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 143.42901,948.63671 c 5.35331,6.77303 19.1946,11.94597 22.82953,13.39994"
id="path4311"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 165.26595,957.07371 c 6.66013,6.3924 -1.50794,5.79645 -6.45182,7.44441"
id="path4313"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 324.08008,958.56259 c 6.84845,-2.46193 19.05646,-11.56821 23.32582,-14.88882"
id="path4315"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 343.93185,943.67377 c 9.80276,-5.09238 3.82905,4.30769 3.97035,4.46665"
id="path4317"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 390.0872,940.696 c 5.64425,8.73302 13.84253,16.324 17.86659,20.34806"
id="path4319"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 407.4575,955.08853 c 7.63943,12.22177 -4.92956,4.92956 -6.94812,6.94812"
id="path4321"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 204.47319,963.02924 c 18.55162,-6.79809 56.78174,1.45336 67.9923,-0.4963"
id="path4323"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 264.0359,957.08112 c 20.67726,4.1454 0.23648,12.24432 -3.47406,14.39253"
id="path4325"
inkscape:connector-curvature="0" />
</g>
</svg>

After

Width:  |  Height:  |  Size: 21 KiB

BIN
presentation2/images/cat_th.pdf

Binary file not shown.

215
presentation2/images/cat_th.svg

@ -0,0 +1,215 @@
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:cc="http://creativecommons.org/ns#"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
width="199.50824"
height="68.025368"
id="svg3945"
version="1.1"
inkscape:version="0.48.2 r9819"
sodipodi:docname="cat_th.svg">
<defs
id="defs3947" />
<sodipodi:namedview
id="base"
pagecolor="#ffffff"
bordercolor="#666666"
borderopacity="1.0"
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="3.515017"
inkscape:cx="100.19026"
inkscape:cy="35.973558"
inkscape:document-units="px"
inkscape:current-layer="layer1"
showgrid="false"
fit-margin-left="1"
fit-margin-top="1"
fit-margin-bottom="1"
fit-margin-right="1"
inkscape:window-width="1280"
inkscape:window-height="752"
inkscape:window-x="0"
inkscape:window-y="0"
inkscape:window-maximized="0" />
<metadata
id="metadata3950">
<rdf:RDF>
<cc:Work
rdf:about="">
<dc:format>image/svg+xml</dc:format>
<dc:type
rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
<dc:title />
</cc:Work>
</rdf:RDF>
</metadata>
<g
inkscape:label="Layer 1"
inkscape:groupmode="layer"
id="layer1"
transform="translate(-34.642066,-962.56786)">
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 39.040506,1014.1881 5.0586,0 0.5664,3.6328 1.58204,0 -1.875,-12.4414 -1.5625,0 -7.16798,12.4414 1.32813,0 2.07031,-3.6328 z m 4.92187,-1.0156 -4.33593,0 1.95312,-3.4571 c 0.23438,-0.4101 1.36719,-2.4804 1.58204,-2.9882 l 0.0195,0 c -0.039,0.4882 0.13672,1.6796 0.19531,2.207 l 0.58594,4.2383 z m 0,0"
id="path3616" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 79.396452,963.56786 -2.65625,12.44141 4.62891,0 c 2.8125,0 5.15625,-1.99219 5.15625,-3.86719 0,-1.26953 -1.11329,-2.36328 -2.8125,-2.63672 1.75781,-0.41015 3.55469,-1.62109 3.55469,-3.26171 0,-1.52344 -1.5625,-2.67579 -3.73048,-2.67579 l -4.14062,0 z m 0.29298,5.42969 0.95702,-4.43359 2.1875,0 c 1.73829,0 3.04687,0.78125 3.04687,1.875 0,1.23046 -1.77733,2.55859 -3.96483,2.55859 l -2.22656,0 z m -1.26954,6.01562 1.03516,-4.9414 2.40234,0 c 1.99218,0 3.22266,0.99609 3.22266,2.1875 0,1.44531 -1.875,2.7539 -3.98437,2.7539 l -2.67579,0 z m 0,0"
id="path3612" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 129.58982,1003.2266 c -1.17187,-0.4883 -2.10937,-0.625 -3.16406,-0.625 -3.96485,0 -7.20704,4.1796 -7.20704,7.9492 0,2.7539 1.83594,4.8633 4.29688,4.8633 1.9336,0 2.63672,-0.1954 3.86719,-0.9766 l 0.15625,-1.25 c -1.21094,0.8008 -1.97265,1.1133 -3.49609,1.1133 -2.22656,0 -3.26173,-1.836 -3.26173,-3.8672 0,-3.1055 2.42188,-6.6992 5.44923,-6.6992 1.21094,0 1.95312,0.3125 2.79296,0.957 l 0.56641,-1.4648 z m 0,0"
id="path3608" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 176.44438,1009.6017 5.44922,-5.8789 -1.66016,0 -4.25781,4.6875 -2.40234,-4.6875 -1.77735,0 3.16406,5.8789 -6.05468,6.5625 1.64062,0 4.94141,-5.4883 2.69532,5.4883 1.79687,0 -3.53516,-6.5625 z m 0,0"
id="path3604" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 157.63514,972.65547 -1.5625,0 -5.35156,6.13281 -2.77344,-6.13281 -1.79687,0 3.39843,7.46094 -1.05468,4.98047 1.5039,0 1.05468,-4.98047 6.58204,-7.46094 z m 0,0"
id="path3600" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 227.75482,1003.12 c 0.13672,-0.1367 0.13672,-0.1758 0.19531,-0.3711 0,-0.039 0.0781,-0.4297 0.0781,-0.5078 l -8.51563,0 -0.21483,1.0938 3.49608,0 c 0.21485,0 0.42969,-0.019 0.64454,-0.019 l 2.42188,0 -8.92579,10.4297 c -0.13671,0.1757 -0.15625,0.2343 -0.19531,0.4101 -0.0195,0.059 -0.0976,0.4297 -0.0976,0.5274 l 8.84765,0 0.25391,-1.1524 -1.67969,0 c -1.54297,0 -3.10547,0.039 -4.64844,0.039 l -0.58593,0 8.92577,-10.4492 z m 0,0"
id="path3596" />
<g
id="g3016"
transform="matrix(0.96567476,-0.25975421,0.25975421,0.96567476,-256.77541,55.180435)">
<path
inkscape:connector-curvature="0"
id="path3986"
d="M 44.170179,993.30318 C 56.741566,990.01272 70.979156,979.95131 77.421887,974.9403"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
inkscape:connector-curvature="0"
id="path3988"
d="m 67.496004,977.42177 c 18.253737,-7.90871 4.897843,4.08153 5.955529,4.96294"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
</g>
<g
id="g3012"
transform="matrix(0.96567476,-0.25975421,0.25975421,0.96567476,-256.77541,55.180435)">
<path
inkscape:connector-curvature="0"
id="path3990"
d="m 94.295887,980.39953 c 1.804741,15.60379 16.331693,27.26547 22.333233,31.26657"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
inkscape:connector-curvature="0"
id="path3992"
d="m 114.64395,1005.2142 c 5.69942,11.6313 -5.08365,5.4747 -6.45183,6.9482"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
</g>
<g
id="g3008"
transform="matrix(0.96567476,-0.25975421,0.25975421,0.96567476,-256.77541,55.180435)">
<path
inkscape:connector-curvature="0"
id="path3994"
d="m 50.125709,1003.2291 c 18.898695,9.7807 38.238182,15.4775 59.059001,17.3703"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
<path
inkscape:connector-curvature="0"
id="path3996"
d="m 105.71065,1017.1253 c 13.67232,6.2007 -2.49483,4.0541 -3.97035,6.4518"
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
</g>
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 159.93954,982.32094 c 3.54461,2.39384 12.64693,11.82131 10.91847,14.39253"
id="path3998"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 166.39878,992.74312 c 5.84478,9.81318 5.9012,-1.21357 8.437,-2.48147"
id="path4000"
inkscape:connector-curvature="0"
sodipodi:nodetypes="cc" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 151.50254,988.27647 c -0.15909,11.60535 5.34315,13.34193 13.39994,17.37033"
id="path4002"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 162.91731,1000.1875 c 5.98705,8.2269 -2.0864,6.6765 -2.48147,7.9408"
id="path4006"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 185.89454,1006.0841 c 6.92086,-2.2792 14.52425,-2.5729 21.77817,-1.8843"
id="path4008"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 204.26175,1005.8146 c 11.02501,1.295 0.13718,-5.339 0.1916,-7.45848"
id="path4010"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 212.04536,1013.9551 c -8.05181,4.8448 -16.44758,2.2928 -23.30629,0.9534"
id="path4012"
inkscape:connector-curvature="0" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 192.88805,1019.1943 c -10.91066,-8.4196 1.92219,-4.2726 3.6425,-8.0963"
id="path4014"
inkscape:connector-curvature="0" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 52.375086,984.84522 1.60156,0 0.17579,-0.8789 -1.6211,0 0.39062,-1.83593 c 0.23438,-1.03517 1.25,-1.15235 1.58204,-1.15235 0.27344,0 0.68359,0.0586 1.11327,0.25391 l 0.21485,-0.9961 c -0.0781,-0.0195 -0.54687,-0.15625 -1.13281,-0.15625 -1.40625,0 -2.63672,1.11329 -2.92968,2.48047 l -0.3125,1.40625 -1.09375,0 -0.17579,0.8789 1.07422,0 -1.21093,5.76176 1.09375,0 1.23046,-5.76176 z m 0,0"
id="path3676" />
<path
inkscape:connector-curvature="0"
style="fill:#000000;fill-opacity:1;stroke:none"
d="m 110.62873,978.75002 c -0.54688,0 -1.34765,0.0586 -2.40234,0.46875 -0.29298,-0.27344 -0.76173,-0.46875 -1.28906,-0.46875 -1.50392,0 -2.91017,1.46485 -2.91017,2.92968 0,0.5274 0.23438,0.957 0.23438,0.957 -0.2539,0.2539 -0.74219,0.8789 -0.74219,1.6602 0,0.4492 0.15625,0.7227 0.17579,0.7617 -0.95704,0.5078 -1.28906,1.3086 -1.28906,1.7969 0,0.918 1.07421,1.7383 2.85156,1.7383 1.5625,0 3.71094,-0.7617 3.71094,-2.461 0,-0.957 -0.60548,-1.6601 -2.61719,-1.6601 l -1.26954,0 c -0.29296,0 -0.70312,0 -0.70312,-0.586 0,-0.1757 0,-0.4101 0.29297,-0.7421 0.23438,0.1953 0.66406,0.4296 1.25,0.4296 1.48438,0 2.91015,-1.4453 2.91015,-2.92964 0,-0.54688 -0.2539,-0.97657 -0.2539,-0.9961 0.0586,0.039 0.0781,0.039 0.0976,0.039 0.0781,0 0.52735,-0.0586 1.15235,-0.0586 0.3125,0 0.42968,0 0.78125,0.0195 l 0.0195,-0.89844 z m -4.53125,4.00388 c -0.625,0 -1.03515,-0.3711 -1.03515,-1.0937 0,-0.87893 0.5664,-2.08987 1.69921,-2.08987 0.39062,0 1.03516,0.17579 1.03516,1.09375 0,0.93752 -0.58594,2.08982 -1.69922,2.08982 z m 0.0195,2.8125 c 0.99608,0 1.77733,0.1953 1.77733,0.8789 0,0.7618 -1.23046,1.3282 -2.46093,1.3282 -1.17188,0 -1.97265,-0.4493 -1.97265,-1.0352 0,-0.2344 0.21483,-1.1719 1.36718,-1.1719 l 1.28907,0 z m 0,0"
id="path3672" />
<g
id="g3023"
transform="translate(-1.4224682,-1.1379746)">
<path
id="path3668"
d="m 79.282019,1020.8874 c -0.546875,0 -1.347649,0.059 -2.402337,0.4688 -0.292975,-0.2735 -0.761725,-0.4688 -1.289062,-0.4688 -1.503913,0 -2.910163,1.4649 -2.910163,2.9297 0,0.5274 0.234375,0.9571 0.234375,0.9571 -0.2539,0.2539 -0.742187,0.8789 -0.742187,1.6601 0,0.4492 0.15625,0.7227 0.175788,0.7617 -0.957038,0.5078 -1.289063,1.3086 -1.289063,1.7969 0,0.918 1.074213,1.7383 2.851562,1.7383 1.5625,0 3.710938,-0.7617 3.710938,-2.461 0,-0.957 -0.605475,-1.6601 -2.617188,-1.6601 l -1.269537,0 c -0.292963,0 -0.703125,0 -0.703125,-0.5859 0,-0.1758 0,-0.4102 0.292975,-0.7422 0.234375,0.1953 0.664062,0.4297 1.25,0.4297 1.484375,0 2.91015,-1.4454 2.91015,-2.9297 0,-0.5469 -0.2539,-0.9766 -0.2539,-0.9961 0.05862,0.039 0.07813,0.039 0.09762,0.039 0.07813,0 0.52735,-0.059 1.15235,-0.059 0.312499,0 0.429687,0 0.781249,0.019 l 0.0195,-0.8984 z m -4.531249,4.0039 c -0.625,0 -1.03515,-0.3711 -1.03515,-1.0937 0,-0.8789 0.5664,-2.0899 1.699212,-2.0899 0.390625,0 1.035163,0.1758 1.035163,1.0938 0,0.9375 -0.585938,2.0898 -1.699225,2.0898 z m 0.0195,2.8125 c 0.996087,0 1.777337,0.1954 1.777337,0.8789 0,0.7618 -1.230462,1.3282 -2.460937,1.3282 -1.171875,0 -1.97265,-0.4492 -1.97265,-1.0352 0,-0.2344 0.214838,-1.1719 1.367187,-1.1719 l 1.289063,0 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3680"
d="m 87.795919,1023.9343 c 0,-1.6016 -1.328125,-2.9101 -2.91015,-2.9101 -1.601563,0 -2.910162,1.3281 -2.910162,2.9101 0,1.582 1.308599,2.8906 2.910162,2.8906 1.582025,0 2.91015,-1.289 2.91015,-2.8906 z m -2.91015,2.3047 c -1.289063,0 -2.304687,-1.0547 -2.304687,-2.3047 0,-1.2695 1.015624,-2.3047 2.304687,-2.3047 1.25,0 2.304687,1.0156 2.304687,2.3047 0,1.2891 -1.054687,2.3047 -2.304687,2.3047 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
<path
id="path3684"
d="m 93.756355,1021.9031 1.601563,0 0.175787,-0.8789 -1.6211,0 0.390625,-1.836 c 0.234375,-1.0351 1.25,-1.1523 1.582038,-1.1523 0.273437,0 0.683587,0.059 1.113275,0.2539 l 0.21485,-0.9961 c -0.07813,-0.019 -0.546875,-0.1563 -1.132813,-0.1563 -1.40625,0 -2.636725,1.1133 -2.929687,2.4805 l -0.3125,1.4063 -1.09375,0 -0.175787,0.8789 1.074225,0 -1.210938,5.7617 1.09375,0 1.230462,-5.7617 z m 0,0"
style="fill:#000000;fill-opacity:1;stroke:none"
inkscape:connector-curvature="0" />
</g>
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="M 189.47277,33.601636 C 219.25653,16.518609 159.62152,-3.0654503 183.4984,34.739611"
id="path3028"
inkscape:connector-curvature="0"
transform="translate(34.642066,962.56786)" />
<path
style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
d="m 183.4984,28.765244 c 1.27899,7.082148 1.56832,7.853466 -4.5519,5.40538"
id="path3030"
inkscape:connector-curvature="0"
transform="translate(34.642066,962.56786)" />
</g>
</svg>

After

Width:  |  Height:  |  Size: 14 KiB

BIN
presentation2/images/simplicial_abgrp.pdf

Binary file not shown.

1260
presentation2/images/simplicial_abgrp.svg

File diff suppressed because it is too large

After

Width:  |  Height:  |  Size: 113 KiB

171
presentation2/presentation.tex

@ -18,7 +18,7 @@
\input{../thesis/preamble}
\graphicspath{ {../presentation2/images/} {../thesis/images/} }
\title{Dold-Kan correspondentie
\title{De Dold-Kan correspondentie
\huge $$ \Ch{\Ab} \simeq \sAb $$}
\author{Joshua Moerman}
\institute[Radboud Universiteit Nijmegen]{Begeleid door Moritz Groth}
@ -31,14 +31,16 @@
\titlepage
\end{frame}
\begin{frame}
\begin{frame}{Categorie\"en}
Een \emph{categorie} $\cat{C}$ bestaat uit
\vspace{5cm}\td{plaatje}
\begin{center}
\includegraphics{cat_th}
\end{center}
met compositie $-\circ-$, zodat
met \emph{compositie} $-\circ-$, zodat
\begin{itemize}
\item er is een identiteit $\id_c: C \to C$ en
\item er is een \emph{identiteit} $\id_c: C \to C$ en
\item compositie is associatief.
\end{itemize}
\end{frame}
@ -52,15 +54,27 @@
\item[$\Ab$]
objecten: abelse groepen \\
pijlen: groupshomomorfismes
\item[$\underline{4}$] \td{diagram}
\item[$\cat{\underline{4}}$]
\tikz[baseline=-0.5ex]{
\matrix (m) [matrix of math nodes, row sep=2em, column sep=2em, ampersand replacement=\&]{
\ast_1 \& \ast_2 \\
\ast_3 \& \ast_4 \\
};
\path[->] (m-1-1) edge node[font=\small, auto] {$ a $} (m-1-2);
\path[->] (m-1-1) edge node[font=\small, auto] {$ f $} (m-2-1);
\path[->] (m-1-2) edge node[font=\small, auto] {$ b $} (m-2-2);
\path[->] (m-2-1) edge node[font=\small, auto] {$ g $} (m-2-2);
} \hspace{1cm} met $ba = gf$.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Functors}
Een \emph{functor} $F$ is een functie van een categorie $\cat{C}$ naar $\cat{D}$ op objecten \'en pijlen.
Een \emph{functor} $F: \cat{C} \to \cat{D}$ is een functie op objecten \'en pijlen.
\vspace{3cm}\td{plaatje}
\begin{center}
\includegraphics[scale=0.9]{cat_functor}
\end{center}
Zodat
\begin{itemize}
@ -79,7 +93,7 @@
Voor een functie $f: V \to W$ definieer
\begin{gather*}
\Z[f]: \Z[V] \to \Z[W] \\
\Z[f](\phi) = \sum_v \phi(v) e_{f(v)}.
\Z[f](\phi) = \sum_v \phi(v) \chi_{\{f(v)\}}.
\end{gather*}
\bigskip
@ -89,7 +103,31 @@
\begin{frame}
\frametitle{Voorbeeld functor}
\td{Commuterend diagram}
Definieer $F: \cat{\underline{4}} \to \Ab$ als volgt:
$$ F(\ast_1) = F(\ast_2) = F(\ast_3) = F(\ast_4) = \Z $$
en op pijlen:
\begin{align*}
F(f)(n) = 4n & & F(g)(n) = 3n \\
F(a)(n) = 6n & & F(b)(n) = 2n.
\end{align*}
\begin{columns}
\begin{column}{0.5\textwidth}
\tikz[baseline=-0.5ex]{
\matrix (m) [matrix of math nodes, row sep=2em, column sep=2em, ampersand replacement=\&]{
\Z \& \Z \\
\Z \& \Z \\
};
\path[->] (m-1-1) edge node[font=\small, auto] {$ \times 6 $} (m-1-2);
\path[->] (m-1-1) edge node[font=\small, auto] {$ \times 4 $} (m-2-1);
\path[->] (m-1-2) edge node[font=\small, auto] {$ \times 2 $} (m-2-2);
\path[->] (m-2-1) edge node[font=\small, auto] {$ \times 3 $} (m-2-2);
}
\end{column}
\begin{column}{0.5\textwidth}
Compositie is behouden, want het diagram commuteert.
\end{column}
\end{columns}
\end{frame}
\begin{frame}
@ -104,42 +142,55 @@
\item Functor $\sim$ Diagrammen.
\end{itemize}
$F$ is \emph{contravariant} (notatie $F: \cat{C}^{op} \to \cat{D}$) als \\
\td{plaatje}
\bigskip\pause
$F$ is \emph{contravariant} (notatie $F: \cat{C}^{op} \to \cat{D}$) als
\begin{columns}
\begin{column}{0.7\textwidth}\includegraphics[scale=0.8]{cat_contrafunctor}\end{column}
\begin{column}{0.3\textwidth}\small $F(g \circ f) = F(g) \circ F(f)$.\end{column}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{D\'e categorie van mijn scriptie}
\frametitle{Belangrijke categorie in mijn scriptie}
\begin{itemize} \item[$\DELTA$]
heeft als objecten $[n] = \{0, \ldots, n\}$, $n\in\N$ \\
en als pijlen monotoon stijgende functies.
objecten: $[n] = \{0, \ldots, n\}$, $n\in\N$ \\
pijlen: monotoon stijgende functies.
\end{itemize}
\bigskip
\only<1>{\begin{example}
Voor elke $n$ zijn er pijlen
Voor elke $n \in \N$ zijn er pijlen
\end{example}}
\only<2->{\begin{lemma}
Elke pijl in $\DELTA$ is een compositie van
\end{lemma}}
\begin{itemize}
\item $\delta_i$\td{Definitie hier}
\item $\sigma_i$
\item $\delta_i: [n] \mono [n+1]$ slaat $i$ over \hfill ($0 \leq i \leq n$)
\item $\sigma_i: [n+1] \epi [n]$ bereik $i$ twee keer \hfill ($0 \leq i < n$)
\end{itemize}
\visible<3>{
Dus $\DELTA = \cdots$\td{Diagram hier}
Dus $\DELTA = \vcenter{\hbox{\includegraphics{delta_cat}}}$
}
\end{frame}
\begin{frame}
\frametitle{D\'e categorie van mijn scriptie}
\frametitle{Belangrijke categorie in mijn scriptie}
$\DELTA = \cdots$\td{Plaatje hier}
$\DELTA = \vcenter{\hbox{\includegraphics[scale=0.8]{delta_cat_geom}}}$
\pause\bigskip
\begin{lemma}
Cosimpliciale gelijkheden\td{dingetjes}
De \emph{cosimpliciale vergelijkingen} gelden:
\small
\begin{align*}
\delta_j\delta_i &= \delta_i\delta_{j-1}, \hspace{1.5cm} \textnormal{ if } i < j,\\
\sigma_j\delta_i &= \delta_i\sigma_{j-1}, \hspace{1.5cm} \textnormal{ if } i < j,\\
\sigma_j\delta_j &= \sigma_j\delta_{j+1} = \id,\\
\sigma_j\delta_i &= \delta_{i-1}\sigma_j, \hspace{1.5cm} \textnormal{ if } i > j+1,\\
\sigma_j\sigma_i &= \sigma_i\sigma_{j+1}, \hspace{1.5cm} \textnormal{ if } i \leq j.
\end{align*}
\end{lemma}
\end{frame}
@ -149,7 +200,22 @@
\bigskip
\visible<2->{
$ A := $\td{diagram}
$$ A :=
\begin{tikzpicture}[baseline=-0.5ex]
\matrix (m) [matrix of math nodes, ampersand replacement=\&, row sep=2em, column sep=2em] {
A_0 \& A_1 \& A_2 \& \cdots \\
};
\draw [raise line=-5, <-] (m-1-1) -> node[font=\small, above] {$ A(\delta_0) $} (m-1-2);
\draw [raise line=5, <-] (m-1-1) -> node[font=\small, below] {$ A(\delta_1) $} (m-1-2);
\foreach \r in {0} \draw [raise line=\r, ->] (m-1-1) -> (m-1-2);
\foreach \r in {-10, 0, 10} \draw [raise line=\r, <-] (m-1-2) -> (m-1-3);
\foreach \r in {-5, 5} \draw [raise line=\r, ->] (m-1-2) -> (m-1-3);
\foreach \r in {-15, -5, 5, 15} \draw [raise line=\r, <-] (m-1-3) -> (m-1-4);
\foreach \r in {-10, 0, 10} \draw [raise line=\r, ->] (m-1-3) -> (m-1-4);
\end{tikzpicture}$$
}
\end{center}
\end{frame}
@ -160,8 +226,17 @@
\item[Objecten] \emph{Simpliciaal abelse groepen} $A$ \\
preciezer: functoren $A: \DELTA^{op} \to \Ab$
\item[Pijlen] \emph{Natuurlijke transformaties} \\
preciezer: $\phi: A \to B$ bestaat uit $\phi_n: A_n \to B_n$ zodat
\vspace{2cm}\td{diagram}
preciezer: $\phi: A \to B$ bestaat uit $\phi_n: A_n \to B_n$ zodat \\
\tikz[baseline=-0.5ex]{
\matrix (m) [matrix of math nodes, row sep=2em, column sep=2em, ampersand replacement=\&]{
A_n \& A_m \\
B_n \& B_m \\
};
\path[->] (m-1-1) edge node[font=\small, auto] {$ A(f) $} (m-1-2);
\path[->] (m-1-1) edge node[font=\small, auto] {$ \phi_n $} (m-2-1);
\path[->] (m-1-2) edge node[font=\small, auto] {$ \phi_m $} (m-2-2);
\path[->] (m-2-1) edge node[font=\small, auto] {$ B(f) $} (m-2-2);
} \hspace{1cm} voor alle $f:[m] \to [n]$.
\end{itemize}
\end{frame}
@ -171,15 +246,24 @@
\item[Objecten] \emph{Ketencomplexen} $C$ \\
preciezer: collectie abelse groepen $C_n$ en groepshomonorfismes $\del_{n+1}: C_{n+1} \to C_n$ zodat $\del \circ \del = 0$
\item[Pijlen] \emph{Ketenafbeeldingen} \\
preciezer: $\phi: C \to D$ bestaat uit $\phi_n: C_n \to D_n$ zodat
\vspace{2cm}\td{diagram}
preciezer: $\phi: C \to D$ bestaat uit $\phi_n: C_n \to D_n$ zodat \\
\tikz[baseline=-0.5ex]{
\matrix (m) [matrix of math nodes, row sep=2em, column sep=2em, ampersand replacement=\&]{
C_{n+1} \& C_n \\
D_{n+1} \& D_n \\
};
\path[->] (m-1-1) edge node[font=\small, auto] {$ \del $} (m-1-2);
\path[->] (m-1-1) edge node[font=\small, auto] {$ \phi_{n+1} $} (m-2-1);
\path[->] (m-1-2) edge node[font=\small, auto] {$ \phi_n $} (m-2-2);
\path[->] (m-2-1) edge node[font=\small, auto] {$ \del $} (m-2-2);
}
\end{itemize}
\end{frame}
\begin{frame}{$\sAb$ lijkt op $\Ch{\Ab}$}
Simpliciaal abelse groepen:
\begin{center}
\includegraphics{simplicial_set} \\
\includegraphics{simplicial_abgrp} \\
met de 5 vergelijkingen
\end{center}
@ -220,18 +304,10 @@ Ketencomplexen:
(want $\sigma_0 \delta_0 = \id$, dus $A(\delta_0)A(\sigma_0) = \id$)
\end{frame}
\begin{frame}{Belangrijke definities}
\begin{frame}{Definities}
Zij $A \in \sAb$ \\
$x \in A_n$ heet een \emph{$n$-simplex} \\
$x$ is \emph{gedegenereerd} als $x = A(\sigma_i)(y)$ voor een zekere $i$ en $y$.
\bigskip\pause
\begin{lemma}
$\forall x \in A_n$ \\
$\exists !$ surjectie $\beta: [n] \epi [m]$ en\\
niet-gedegenereerde $y \in A_m$ zodat
$$ x = A(\beta)(y). $$
\end{lemma}
$x \in A_n$ is \emph{gedegenereerd} als $x = A(\sigma_i)(y)$ voor een zekere $i$ en $y$.
\end{frame}
\begin{frame}{De juiste constructie}
@ -240,20 +316,31 @@ Ketencomplexen:
N(A)_n &= \bigcap_{i=1}^n \ker(A(\delta_i)) \\
\del &= A(\delta_0)
\end{align*}
\bigskip\pause
\pause
\begin{lemma}
$x \in N(A)_n$ is niet-gedegenereerd.
\end{lemma}
\bigskip
\begin{lemma}
Sterker nog:
$$ A_n = N(A)_n \oplus D_n(A). $$
\centering$ A_n = N(A)_n \oplus D_n(A). $
\end{lemma}
\end{frame}
\begin{frame}{Voorbeeld}
Definieer de volgende simpliciaal abelse groep:
\begin{gather*}
A_n = \Z \\
A(\delta_i) = A(\sigma_i) = \id.
\end{gather*}
\pause
$$ N(A) = \Z \from 0 \from 0 \from \cdots. $$
\end{frame}
\begin{frame}
\begin{center}
$$ N: \sAb \rightleftarrows \Ch{\Ab} :K $$
\pause\bigskip
\Huge Vragen?
\end{center}
\end{frame}

6
presentation2/symbols.tex

@ -16,7 +16,11 @@
\begin{frame}
$$ \cat{C} \cat{D} $$
$$ A B C X Y Z $$
$$ F(A) F(B) F(C) $$
\small $$ f g g \circ f $$
\small $$ F(f) F(g) $$
\end{frame}
\end{document}