sAb: updated a picture

12 years ago · 35e2abd1fa
6 changed files with 101 additions and 89 deletions
--- a/thesis/3_SimplicialAbelianGroups.tex
+++ b/thesis/3_SimplicialAbelianGroups.tex
@ -39,12 +39,12 @@ This category $\DELTA$ will act as a protoype for these kind of geometric struct
 	(Or equivalently a covariant functor $X: \DELTA^{op} \to \Set.$)
 \end{definition}

-So the category of all simplicial sets, $\sSet$, is the functor category $\Set^{\DELTA^{op}}$, where morphisms are natural transformations. Because the face and degeneracy maps give all the maps in $\DELTA$ it is sufficient to define images of $\delta_i$ and $\sigma_i$ in order to define a functor $X: \DELTA^{op} \to \Set$. And hence we can picture a simplicial set as done in figure~\ref{fig:simplicial_abelian_group}. Comparing this to figure~\ref{fig:delta_cat} we see that the arrows are reversed, because $X$ is a contravariant functor.
+So the category of all simplicial sets, $\sSet$, is the functor category $\Set^{\DELTA^{op}}$, where morphisms are natural transformations. Because the face and degeneracy maps give all the maps in $\DELTA$ it is sufficient to define images of $\delta_i$ and $\sigma_i$ in order to define a functor $X: \DELTA^{op} \to \Set$. And hence we can picture a simplicial set as done in figure~\ref{fig:simplicial_set}. Comparing this to figure~\ref{fig:delta_cat} we see that the arrows are reversed, because $X$ is a contravariant functor.

 \begin{figure}
-	\includegraphics{simplicial_abelian_group}
-	\caption{A simplicial abelian group.}
-	\label{fig:simplicial_abelian_group}
+	\includegraphics{simplicial_set}
+	\caption{A simplicial set.}
+	\label{fig:simplicial_set}
 \end{figure}


--- a/thesis/images/delta_cat.pdf
+++ b/thesis/images/delta_cat.pdf
--- a/thesis/images/delta_cat.svg
+++ b/thesis/images/delta_cat.svg
@ -13,7 +13,7 @@
   version="1.1"
   id="svg4102"
   inkscape:version="0.48.2 r9819"
-   sodipodi:docname="thesissymbols.svg">
+   sodipodi:docname="delta_cat.svg">
  <metadata
     id="metadata5179">
    <rdf:RDF>
@ -22,7 +22,7 @@
        <dc:format>image/svg+xml</dc:format>
        <dc:type
           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
-        <dc:title></dc:title>
+        <dc:title />
      </cc:Work>
    </rdf:RDF>
  </metadata>
@ -47,7 +47,7 @@
     inkscape:cx="117.00119"
     inkscape:cy="49.609396"
     inkscape:window-x="0"
-     inkscape:window-y="0"
+     inkscape:window-y="626"
     inkscape:window-maximized="0"
     inkscape:current-layer="svg4102" />
  <defs
@ -1171,20 +1171,6 @@
       style="fill:#000000;fill-opacity:1;stroke:none"
       inkscape:connector-curvature="0" />
  </g>
-  <g
-     id="g7669"
-     transform="translate(-120.65262,-397.10063)">
-    <path
-       id="path6126"
-       d="m 156.00337,424.53826 c -1.53125,0.375 -2.625,1.96875 -2.625,3.35937 0,1.28125 0.85938,2 1.8125,2 1.40625,0 2.35938,-1.9375 2.35938,-3.51562 0,-1.07813 -0.5,-1.73438 -0.79688,-2.14063 -0.4375,-0.5625 -1.15625,-1.48437 -1.15625,-2.04687 0,-0.20313 0.15625,-0.5625 0.67188,-0.5625 0.375,0 0.60937,0.125 0.96875,0.32812 0.10937,0.0781 0.375,0.23438 0.53125,0.23438 0.25,0 0.4375,-0.25 0.4375,-0.45313 0,-0.21875 -0.1875,-0.25 -0.60938,-0.34375 -0.5625,-0.125 -0.71875,-0.125 -0.92187,-0.125 -0.20313,0 -1.375,0 -1.375,1.21875 0,0.57813 0.29687,1.26563 0.70312,2.04688 z m 0.125,0.23437 c 0.45313,0.9375 0.64063,1.29688 0.64063,2.07813 0,0.9375 -0.5,2.8125 -1.5625,2.8125 -0.46875,0 -1.14063,-0.3125 -1.14063,-1.42188 0,-0.78125 0.4375,-3.03125 2.0625,-3.46875 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-    <path
-       id="path6122"
-       d="m 160.453,426.58226 c 0,-0.17188 -0.125,-0.3125 -0.3125,-0.3125 -0.20313,0 -0.4375,0.20312 -0.4375,0.4375 0,0.17187 0.125,0.29687 0.3125,0.29687 0.20312,0 0.4375,-0.1875 0.4375,-0.42187 z m -1.15625,2.92187 -0.4375,1.09375 c -0.0469,0.125 -0.0781,0.21875 -0.0781,0.35938 0,0.39062 0.29688,0.67187 0.71875,0.67187 0.78125,0 1.10938,-1.10937 1.10938,-1.21875 0,-0.0781 -0.0625,-0.10937 -0.125,-0.10937 -0.0937,0 -0.10938,0.0625 -0.14063,0.14062 -0.17187,0.64063 -0.5,0.96875 -0.82812,0.96875 -0.0937,0 -0.1875,-0.0469 -0.1875,-0.25 0,-0.20312 0.0625,-0.34375 0.15625,-0.59375 0.0781,-0.20312 0.15625,-0.42187 0.25,-0.64062 l 0.25,-0.64063 c 0.0625,-0.1875 0.17187,-0.4375 0.17187,-0.57812 0,-0.39063 -0.32812,-0.67188 -0.73437,-0.67188 -0.76563,0 -1.10938,1.10938 -1.10938,1.21875 0,0.0781 0.0625,0.10938 0.125,0.10938 0.10938,0 0.10938,-0.0469 0.14063,-0.125 0.21875,-0.76563 0.57812,-0.98438 0.82812,-0.98438 0.10938,0 0.1875,0.0469 0.1875,0.26563 0,0.0781 -0.0156,0.1875 -0.0937,0.4375 l -0.20312,0.54687 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-  </g>
  <g
     id="g7707"
     transform="translate(-172.17385,-297.90063)">
--- a/thesis/images/simplicial_abelian_group.pdf
+++ b/thesis/images/simplicial_abelian_group.pdf
--- a/thesis/images/simplicial_set.pdf
+++ b/thesis/images/simplicial_set.pdf
--- a/thesis/images/simplicial_abelian_group.svg
+++ b/thesis/images/simplicial_abelian_group.svg
@ -13,7 +13,7 @@
   version="1.1"
   id="svg4102"
   inkscape:version="0.48.2 r9819"
-   sodipodi:docname="simplicial_abelian_group.svg">
+   sodipodi:docname="simplicial_set.svg">
  <metadata
     id="metadata5179">
    <rdf:RDF>
@ -22,7 +22,7 @@
        <dc:format>image/svg+xml</dc:format>
        <dc:type
           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
-        <dc:title></dc:title>
+        <dc:title />
      </cc:Work>
    </rdf:RDF>
  </metadata>
@ -43,11 +43,11 @@
     fit-margin-top="1"
     fit-margin-right="1"
     fit-margin-bottom="1"
-     inkscape:zoom="2.1649824"
-     inkscape:cx="117.00119"
-     inkscape:cy="49.609396"
+     inkscape:zoom="4.0400329"
+     inkscape:cx="128.75472"
+     inkscape:cy="33.512817"
     inkscape:window-x="0"
-     inkscape:window-y="0"
+     inkscape:window-y="626"
     inkscape:window-maximized="0"
     inkscape:current-layer="svg4102" />
  <defs
@ -1095,20 +1095,6 @@
       style="fill:#000000;fill-opacity:1;stroke:none"
       inkscape:connector-curvature="0" />
  </g>
-  <g
-     id="g7669"
-     transform="translate(-120.65262,-395.50063)">
-    <path
-       id="path6126"
-       d="m 156.00337,424.53826 c -1.53125,0.375 -2.625,1.96875 -2.625,3.35937 0,1.28125 0.85938,2 1.8125,2 1.40625,0 2.35938,-1.9375 2.35938,-3.51562 0,-1.07813 -0.5,-1.73438 -0.79688,-2.14063 -0.4375,-0.5625 -1.15625,-1.48437 -1.15625,-2.04687 0,-0.20313 0.15625,-0.5625 0.67188,-0.5625 0.375,0 0.60937,0.125 0.96875,0.32812 0.10937,0.0781 0.375,0.23438 0.53125,0.23438 0.25,0 0.4375,-0.25 0.4375,-0.45313 0,-0.21875 -0.1875,-0.25 -0.60938,-0.34375 -0.5625,-0.125 -0.71875,-0.125 -0.92187,-0.125 -0.20313,0 -1.375,0 -1.375,1.21875 0,0.57813 0.29687,1.26563 0.70312,2.04688 z m 0.125,0.23437 c 0.45313,0.9375 0.64063,1.29688 0.64063,2.07813 0,0.9375 -0.5,2.8125 -1.5625,2.8125 -0.46875,0 -1.14063,-0.3125 -1.14063,-1.42188 0,-0.78125 0.4375,-3.03125 2.0625,-3.46875 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-    <path
-       id="path6122"
-       d="m 160.453,426.58226 c 0,-0.17188 -0.125,-0.3125 -0.3125,-0.3125 -0.20313,0 -0.4375,0.20312 -0.4375,0.4375 0,0.17187 0.125,0.29687 0.3125,0.29687 0.20312,0 0.4375,-0.1875 0.4375,-0.42187 z m -1.15625,2.92187 -0.4375,1.09375 c -0.0469,0.125 -0.0781,0.21875 -0.0781,0.35938 0,0.39062 0.29688,0.67187 0.71875,0.67187 0.78125,0 1.10938,-1.10937 1.10938,-1.21875 0,-0.0781 -0.0625,-0.10937 -0.125,-0.10937 -0.0937,0 -0.10938,0.0625 -0.14063,0.14062 -0.17187,0.64063 -0.5,0.96875 -0.82812,0.96875 -0.0937,0 -0.1875,-0.0469 -0.1875,-0.25 0,-0.20312 0.0625,-0.34375 0.15625,-0.59375 0.0781,-0.20312 0.15625,-0.42187 0.25,-0.64062 l 0.25,-0.64063 c 0.0625,-0.1875 0.17187,-0.4375 0.17187,-0.57812 0,-0.39063 -0.32812,-0.67188 -0.73437,-0.67188 -0.76563,0 -1.10938,1.10938 -1.10938,1.21875 0,0.0781 0.0625,0.10938 0.125,0.10938 0.10938,0 0.10938,-0.0469 0.14063,-0.125 0.21875,-0.76563 0.57812,-0.98438 0.82812,-0.98438 0.10938,0 0.1875,0.0469 0.1875,0.26563 0,0.0781 -0.0156,0.1875 -0.0937,0.4375 l -0.20312,0.54687 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-  </g>
  <g
     id="g7707"
     transform="matrix(-1,0,0,1,248.95854,-297.90063)">
@ -1212,59 +1198,99 @@
       inkscape:connector-curvature="0" />
  </g>
  <g
-     id="g12117"
-     transform="translate(-34.513244,88.314808)">
-    <path
-       id="path11762"
-       d="m 37.139005,-67.831754 c -0.42188,0.70313 -0.82813,0.953131 -1.39063,0.98438 -0.14062,0.0156 -0.23437,0.0156 -0.23437,0.218751 0,0.0781 0.0625,0.125 0.14062,0.125 0.21875,0 0.75,-0.0312 0.96875,-0.0312 0.34375,0 0.73438,0.0312 1.0625,0.0312 0.0781,0 0.21875,0 0.21875,-0.23438 0,-0.0937 -0.0937,-0.109371 -0.17187,-0.109371 -0.26563,-0.0312 -0.5,-0.125 -0.5,-0.40625 0,-0.17188 0.0781,-0.29688 0.23437,-0.5625 l 0.90625,-1.51563 3.04688,0 c 0.0156,0.10938 0.0156,0.20313 0.0156,0.3125 0.0469,0.3125 0.1875,1.5625 0.1875,1.78125 0,0.359381 -0.60937,0.39063 -0.79687,0.39063 -0.14063,0 -0.26563,0 -0.26563,0.218751 0,0.125 0.10938,0.125 0.17188,0.125 0.20312,0 0.45312,-0.0312 0.65625,-0.0312 l 0.67187,0 c 0.73438,0 1.26563,0.0312 1.26563,0.0312 0.0937,0 0.218751,0 0.218751,-0.23438 0,-0.109371 -0.109381,-0.109371 -0.281251,-0.109371 -0.65625,0 -0.67188,-0.10938 -0.70313,-0.46875 l -0.73437,-7.45313 c -0.0312,-0.25 -0.0781,-0.26562 -0.20313,-0.26562 -0.125,0 -0.1875,0.0156 -0.29687,0.20312 l -4.1875,7 z m 1.4375,-1.84375 2.40625,-4.01562 0.40625,4.01562 -2.8125,0 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-    <path
-       id="path11766"
-       d="m 47.774375,-67.257504 c 0,-0.84375 -0.0781,-1.35937 -0.34375,-1.875 -0.34375,-0.70312 -1,-0.875 -1.4375,-0.875 -1,0 -1.375,0.75 -1.48437,0.96875 -0.28125,0.57813 -0.29688,1.375 -0.29688,1.78125 0,0.53125 0.0156,1.32813 0.40625,1.96875 0.35938,0.59375 0.95313,0.750001 1.375,0.750001 0.39063,0 1.0625,-0.125 1.46875,-0.906251 0.29688,-0.578119 0.3125,-1.29687 0.3125,-1.8125 z m -1.78125,2.484381 c -0.26562,0 -0.8125,-0.125 -0.98437,-0.953131 -0.0937,-0.45312 -0.0937,-1.20312 -0.0937,-1.625 0,-0.54687 0,-1.10937 0.0937,-1.54687 0.17187,-0.8125 0.78125,-0.89063 0.98437,-0.89063 0.26563,0 0.82813,0.14063 0.98438,0.85938 0.0937,0.4375 0.0937,1.04687 0.0937,1.57812 0,0.46875 0,1.1875 -0.0937,1.640631 -0.17188,0.828119 -0.71875,0.9375 -0.98438,0.9375 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
+     transform="translate(-241.14743,-102.94531)"
+     id="g3329">
+    <g
+       transform="translate(240.847,124.938)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3195">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 5.671875,-4.859375 -1.125,-2.609375 C 4.703125,-7.75 5.0625,-7.8125 5.21875,-7.8125 c 0.0625,0 0.203125,-0.015625 0.203125,-0.21875 0,-0.125 -0.109375,-0.125 -0.1875,-0.125 -0.203125,0 -0.4375,0.015625 -0.640625,0.015625 l -0.703125,0 c -0.71875,0 -1.25,-0.015625 -1.265625,-0.015625 -0.09375,0 -0.203125,0 -0.203125,0.21875 0,0.125 0.09375,0.125 0.25,0.125 0.703125,0 0.75,0.109375 0.859375,0.40625 l 1.421875,3.3125 -2.59375,2.78125 C 1.9375,-0.84375 1.421875,-0.390625 0.53125,-0.34375 0.390625,-0.328125 0.296875,-0.328125 0.296875,-0.125 0.296875,-0.078125 0.3125,0 0.4375,0 0.609375,0 0.78125,-0.03125 0.953125,-0.03125 l 0.5625,0 C 1.90625,-0.03125 2.3125,0 2.6875,0 c 0.078125,0 0.234375,0 0.234375,-0.21875 0,-0.109375 -0.09375,-0.125 -0.15625,-0.125 -0.25,-0.03125 -0.40625,-0.15625 -0.40625,-0.34375 0,-0.203125 0.15625,-0.359375 0.5,-0.71875 l 1.0625,-1.15625 C 4.1875,-2.828125 4.8125,-3.53125 5.078125,-3.796875 l 1.25,2.953125 c 0.015625,0.015625 0.0625,0.140625 0.0625,0.15625 0,0.109375 -0.265625,0.3125 -0.640625,0.34375 -0.078125,0 -0.203125,0.015625 -0.203125,0.21875 C 5.546875,0 5.671875,0 5.71875,0 5.921875,0 6.171875,-0.03125 6.375,-0.03125 l 1.3125,0 C 7.90625,-0.03125 8.125,0 8.328125,0 c 0.09375,0 0.21875,0 0.21875,-0.234375 0,-0.109375 -0.125,-0.109375 -0.234375,-0.109375 C 7.609375,-0.359375 7.578125,-0.421875 7.375,-0.859375 L 5.796875,-4.5625 7.3125,-6.1875 c 0.125,-0.125 0.390625,-0.421875 0.5,-0.546875 0.515625,-0.53125 1,-1.015625 1.96875,-1.078125 0.109375,-0.015625 0.234375,-0.015625 0.234375,-0.21875 0,-0.125 -0.109375,-0.125 -0.15625,-0.125 -0.171875,0 -0.34375,0.015625 -0.515625,0.015625 l -0.546875,0 C 8.421875,-8.140625 8,-8.15625 7.625,-8.15625 c -0.078125,0 -0.21875,0 -0.21875,0.203125 0,0.125 0.078125,0.140625 0.140625,0.140625 0.203125,0.015625 0.40625,0.109375 0.40625,0.34375 L 7.9375,-7.453125 C 7.921875,-7.359375 7.90625,-7.25 7.765625,-7.09375 l -2.09375,2.234375 z m 0,0"
+         id="path3283" />
+    </g>
+    <g
+       transform="translate(250.563,126.732)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3199">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 3.890625,-2.546875 c 0,-0.84375 -0.078125,-1.359375 -0.34375,-1.875 -0.34375,-0.703125 -1,-0.875 -1.4375,-0.875 -1,0 -1.375,0.75 -1.484375,0.96875 -0.28125,0.578125 -0.296875,1.375 -0.296875,1.78125 0,0.53125 0.015625,1.328125 0.40625,1.96875 0.359375,0.59375 0.953125,0.75 1.375,0.75 0.390625,0 1.0625,-0.125 1.46875,-0.90625 0.296875,-0.578125 0.3125,-1.296875 0.3125,-1.8125 z M 2.109375,-0.0625 C 1.84375,-0.0625 1.296875,-0.1875 1.125,-1.015625 1.03125,-1.46875 1.03125,-2.21875 1.03125,-2.640625 1.03125,-3.1875 1.03125,-3.75 1.125,-4.1875 1.296875,-5 1.90625,-5.078125 2.109375,-5.078125 c 0.265625,0 0.828125,0.140625 0.984375,0.859375 0.09375,0.4375 0.09375,1.046875 0.09375,1.578125 0,0.46875 0,1.1875 -0.09375,1.640625 -0.171875,0.828125 -0.71875,0.9375 -0.984375,0.9375 z m 0,0"
+         id="path3287" />
+    </g>
  </g>
  <g
-     id="g12121"
-     transform="translate(-2.7092218,88.400743)">
-    <path
-       id="path11774"
-       d="m 69.243995,-67.831754 c -0.42188,0.70313 -0.828129,0.953131 -1.390629,0.98438 -0.14062,0.0156 -0.234371,0.0156 -0.234371,0.218751 0,0.0781 0.0625,0.125 0.14062,0.125 0.218751,0 0.75,-0.0312 0.968751,-0.0312 0.343749,0 0.73438,0.0312 1.0625,0.0312 0.0781,0 0.218749,0 0.218749,-0.23438 0,-0.0937 -0.0937,-0.109371 -0.171869,-0.109371 -0.265631,-0.0312 -0.5,-0.125 -0.5,-0.40625 0,-0.17188 0.0781,-0.29688 0.234369,-0.5625 l 0.906251,-1.51563 3.04688,0 c 0.0156,0.10938 0.0156,0.20313 0.0156,0.3125 0.0469,0.3125 0.1875,1.5625 0.1875,1.78125 0,0.359381 -0.609371,0.39063 -0.796871,0.39063 -0.140629,0 -0.265629,0 -0.265629,0.218751 0,0.125 0.10938,0.125 0.17188,0.125 0.20312,0 0.45312,-0.0312 0.656249,-0.0312 l 0.671871,0 c 0.73438,0 1.26563,0.0312 1.26563,0.0312 0.0937,0 0.21875,0 0.21875,-0.23438 0,-0.109371 -0.10938,-0.109371 -0.281251,-0.109371 -0.656249,0 -0.67188,-0.10938 -0.703129,-0.46875 l -0.734371,-7.45313 c -0.0312,-0.25 -0.0781,-0.26562 -0.203129,-0.26562 -0.125,0 -0.1875,0.0156 -0.296871,0.20312 l -4.1875,7 z m 1.4375,-1.84375 2.406251,-4.01562 0.406249,4.01562 -2.8125,0 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-    <path
-       id="path11778"
-       d="m 78.487736,-69.788754 c 0,-0.21875 -0.0156,-0.21875 -0.23438,-0.21875 -0.32812,0.3125 -0.75,0.5 -1.5,0.5 l 0,0.26563 c 0.21875,0 0.64063,0 1.10938,-0.20313 l 0,4.07813 c 0,0.29687 -0.0312,0.390621 -0.78125,0.390621 l -0.28125,0 0,0.26563 c 0.32812,-0.0312 1.01562,-0.0312 1.375,-0.0312 0.35937,0 1.04687,0 1.375,0.0312 l 0,-0.26563 -0.28125,0 c -0.75,0 -0.78125,-0.0937 -0.78125,-0.390621 l 0,-4.42188 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
+     transform="translate(-210.11118,-102.99289)"
+     id="g3335">
+    <g
+       transform="translate(273.892,124.938)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3207">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 5.671875,-4.859375 -1.125,-2.609375 C 4.703125,-7.75 5.0625,-7.8125 5.21875,-7.8125 c 0.0625,0 0.203125,-0.015625 0.203125,-0.21875 0,-0.125 -0.109375,-0.125 -0.1875,-0.125 -0.203125,0 -0.4375,0.015625 -0.640625,0.015625 l -0.703125,0 c -0.71875,0 -1.25,-0.015625 -1.265625,-0.015625 -0.09375,0 -0.203125,0 -0.203125,0.21875 0,0.125 0.09375,0.125 0.25,0.125 0.703125,0 0.75,0.109375 0.859375,0.40625 l 1.421875,3.3125 -2.59375,2.78125 C 1.9375,-0.84375 1.421875,-0.390625 0.53125,-0.34375 0.390625,-0.328125 0.296875,-0.328125 0.296875,-0.125 0.296875,-0.078125 0.3125,0 0.4375,0 0.609375,0 0.78125,-0.03125 0.953125,-0.03125 l 0.5625,0 C 1.90625,-0.03125 2.3125,0 2.6875,0 c 0.078125,0 0.234375,0 0.234375,-0.21875 0,-0.109375 -0.09375,-0.125 -0.15625,-0.125 -0.25,-0.03125 -0.40625,-0.15625 -0.40625,-0.34375 0,-0.203125 0.15625,-0.359375 0.5,-0.71875 l 1.0625,-1.15625 C 4.1875,-2.828125 4.8125,-3.53125 5.078125,-3.796875 l 1.25,2.953125 c 0.015625,0.015625 0.0625,0.140625 0.0625,0.15625 0,0.109375 -0.265625,0.3125 -0.640625,0.34375 -0.078125,0 -0.203125,0.015625 -0.203125,0.21875 C 5.546875,0 5.671875,0 5.71875,0 5.921875,0 6.171875,-0.03125 6.375,-0.03125 l 1.3125,0 C 7.90625,-0.03125 8.125,0 8.328125,0 c 0.09375,0 0.21875,0 0.21875,-0.234375 0,-0.109375 -0.125,-0.109375 -0.234375,-0.109375 C 7.609375,-0.359375 7.578125,-0.421875 7.375,-0.859375 L 5.796875,-4.5625 7.3125,-6.1875 c 0.125,-0.125 0.390625,-0.421875 0.5,-0.546875 0.515625,-0.53125 1,-1.015625 1.96875,-1.078125 0.109375,-0.015625 0.234375,-0.015625 0.234375,-0.21875 0,-0.125 -0.109375,-0.125 -0.15625,-0.125 -0.171875,0 -0.34375,0.015625 -0.515625,0.015625 l -0.546875,0 C 8.421875,-8.140625 8,-8.15625 7.625,-8.15625 c -0.078125,0 -0.21875,0 -0.21875,0.203125 0,0.125 0.078125,0.140625 0.140625,0.140625 0.203125,0.015625 0.40625,0.109375 0.40625,0.34375 L 7.9375,-7.453125 C 7.921875,-7.359375 7.90625,-7.25 7.765625,-7.09375 l -2.09375,2.234375 z m 0,0"
+         id="path3295" />
+    </g>
+    <g
+       transform="translate(283.60699,126.732)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3211">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 2.5,-5.078125 c 0,-0.21875 -0.015625,-0.21875 -0.234375,-0.21875 -0.328125,0.3125 -0.75,0.5 -1.5,0.5 l 0,0.265625 c 0.21875,0 0.640625,0 1.109375,-0.203125 l 0,4.078125 c 0,0.296875 -0.03125,0.390625 -0.78125,0.390625 l -0.28125,0 0,0.265625 c 0.328125,-0.03125 1.015625,-0.03125 1.375,-0.03125 0.359375,0 1.046875,0 1.375,0.03125 l 0,-0.265625 -0.28125,0 c -0.75,0 -0.78125,-0.09375 -0.78125,-0.390625 l 0,-4.421875 z m 0,0"
+         id="path3299" />
+    </g>
  </g>
  <g
-     id="g12125"
-     transform="translate(28.766655,88.400743)">
-    <path
-       id="path11786"
-       d="m 101.348,-67.831754 c -0.42188,0.70313 -0.82813,0.953131 -1.390634,0.98438 -0.14062,0.0156 -0.23437,0.0156 -0.23437,0.218751 0,0.0781 0.0625,0.125 0.14062,0.125 0.218754,0 0.750004,-0.0312 0.968754,-0.0312 0.34375,0 0.73438,0.0312 1.0625,0.0312 0.0781,0 0.21875,0 0.21875,-0.23438 0,-0.0937 -0.0937,-0.109371 -0.17187,-0.109371 -0.26563,-0.0312 -0.5,-0.125 -0.5,-0.40625 0,-0.17188 0.0781,-0.29688 0.23437,-0.5625 l 0.90625,-1.51563 3.04688,0 c 0.0156,0.10938 0.0156,0.20313 0.0156,0.3125 0.0469,0.3125 0.1875,1.5625 0.1875,1.78125 0,0.359381 -0.60937,0.39063 -0.79687,0.39063 -0.14063,0 -0.26563,0 -0.26563,0.218751 0,0.125 0.10938,0.125 0.17188,0.125 0.20312,0 0.45312,-0.0312 0.65625,-0.0312 l 0.67187,0 c 0.73438,0 1.26563,0.0312 1.26563,0.0312 0.0937,0 0.21875,0 0.21875,-0.23438 0,-0.109371 -0.10938,-0.109371 -0.28125,-0.109371 -0.65625,0 -0.67188,-0.10938 -0.70313,-0.46875 l -0.73437,-7.45313 c -0.0312,-0.25 -0.0781,-0.26562 -0.20313,-0.26562 -0.125,0 -0.1875,0.0156 -0.29687,0.20312 l -4.1875,7 z m 1.4375,-1.84375 2.40625,-4.01562 0.40625,4.01562 -2.8125,0 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-    <path
-       id="path11790"
-       d="m 110.34276,-66.335623 c 0.125,-0.125 0.45313,-0.390631 0.59375,-0.5 0.48438,-0.453131 0.95313,-0.890631 0.95313,-1.609381 0,-0.95312 -0.79688,-1.5625 -1.78125,-1.5625 -0.96875,0 -1.59375,0.71875 -1.59375,1.4375 0,0.39063 0.3125,0.4375 0.42187,0.4375 0.17188,0 0.42188,-0.10937 0.42188,-0.42187 0,-0.40625 -0.40625,-0.40625 -0.5,-0.40625 0.23437,-0.59375 0.76562,-0.78125 1.15625,-0.78125 0.73437,0 1.125,0.625 1.125,1.29687 0,0.82813 -0.57813,1.4375 -1.53125,2.39063 l -1,1.04687 c -0.0937,0.0781 -0.0937,0.0937 -0.0937,0.296881 l 3.14062,0 0.23438,-1.421881 -0.25,0 c -0.0156,0.15625 -0.0781,0.546881 -0.17188,0.70313 -0.0469,0.0625 -0.65625,0.0625 -0.78125,0.0625 l -1.42187,0 1.07812,-0.968749 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
+     transform="translate(-179.7478,-102.93373)"
+     id="g3341">
+    <g
+       transform="translate(306.936,124.938)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3219">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 5.671875,-4.859375 -1.125,-2.609375 C 4.703125,-7.75 5.0625,-7.8125 5.21875,-7.8125 c 0.0625,0 0.203125,-0.015625 0.203125,-0.21875 0,-0.125 -0.109375,-0.125 -0.1875,-0.125 -0.203125,0 -0.4375,0.015625 -0.640625,0.015625 l -0.703125,0 c -0.71875,0 -1.25,-0.015625 -1.265625,-0.015625 -0.09375,0 -0.203125,0 -0.203125,0.21875 0,0.125 0.09375,0.125 0.25,0.125 0.703125,0 0.75,0.109375 0.859375,0.40625 l 1.421875,3.3125 -2.59375,2.78125 C 1.9375,-0.84375 1.421875,-0.390625 0.53125,-0.34375 0.390625,-0.328125 0.296875,-0.328125 0.296875,-0.125 0.296875,-0.078125 0.3125,0 0.4375,0 0.609375,0 0.78125,-0.03125 0.953125,-0.03125 l 0.5625,0 C 1.90625,-0.03125 2.3125,0 2.6875,0 c 0.078125,0 0.234375,0 0.234375,-0.21875 0,-0.109375 -0.09375,-0.125 -0.15625,-0.125 -0.25,-0.03125 -0.40625,-0.15625 -0.40625,-0.34375 0,-0.203125 0.15625,-0.359375 0.5,-0.71875 l 1.0625,-1.15625 C 4.1875,-2.828125 4.8125,-3.53125 5.078125,-3.796875 l 1.25,2.953125 c 0.015625,0.015625 0.0625,0.140625 0.0625,0.15625 0,0.109375 -0.265625,0.3125 -0.640625,0.34375 -0.078125,0 -0.203125,0.015625 -0.203125,0.21875 C 5.546875,0 5.671875,0 5.71875,0 5.921875,0 6.171875,-0.03125 6.375,-0.03125 l 1.3125,0 C 7.90625,-0.03125 8.125,0 8.328125,0 c 0.09375,0 0.21875,0 0.21875,-0.234375 0,-0.109375 -0.125,-0.109375 -0.234375,-0.109375 C 7.609375,-0.359375 7.578125,-0.421875 7.375,-0.859375 L 5.796875,-4.5625 7.3125,-6.1875 c 0.125,-0.125 0.390625,-0.421875 0.5,-0.546875 0.515625,-0.53125 1,-1.015625 1.96875,-1.078125 0.109375,-0.015625 0.234375,-0.015625 0.234375,-0.21875 0,-0.125 -0.109375,-0.125 -0.15625,-0.125 -0.171875,0 -0.34375,0.015625 -0.515625,0.015625 l -0.546875,0 C 8.421875,-8.140625 8,-8.15625 7.625,-8.15625 c -0.078125,0 -0.21875,0 -0.21875,0.203125 0,0.125 0.078125,0.140625 0.140625,0.140625 0.203125,0.015625 0.40625,0.109375 0.40625,0.34375 L 7.9375,-7.453125 C 7.921875,-7.359375 7.90625,-7.25 7.765625,-7.09375 l -2.09375,2.234375 z m 0,0"
+         id="path3307" />
+    </g>
+    <g
+       transform="translate(316.651,126.732)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3223">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 2.25,-1.625 c 0.125,-0.125 0.453125,-0.390625 0.59375,-0.5 0.484375,-0.453125 0.953125,-0.890625 0.953125,-1.609375 0,-0.953125 -0.796875,-1.5625 -1.78125,-1.5625 -0.96875,0 -1.59375,0.71875 -1.59375,1.4375 0,0.390625 0.3125,0.4375 0.421875,0.4375 0.171875,0 0.421875,-0.109375 0.421875,-0.421875 0,-0.40625 -0.40625,-0.40625 -0.5,-0.40625 C 1,-4.84375 1.53125,-5.03125 1.921875,-5.03125 c 0.734375,0 1.125,0.625 1.125,1.296875 0,0.828125 -0.578125,1.4375 -1.53125,2.390625 l -1,1.046875 C 0.421875,-0.21875 0.421875,-0.203125 0.421875,0 l 3.140625,0 0.234375,-1.421875 -0.25,0 C 3.53125,-1.265625 3.46875,-0.875 3.375,-0.71875 c -0.046875,0.0625 -0.65625,0.0625 -0.78125,0.0625 l -1.421875,0 L 2.25,-1.625 z m 0,0"
+         id="path3311" />
+    </g>
  </g>
  <g
-     id="g12129"
-     transform="translate(60.477017,88.314808)">
-    <path
-       id="path11798"
-       d="m 133.45298,-67.831754 c -0.42186,0.70313 -0.82811,0.953131 -1.39061,0.98438 -0.14063,0.0156 -0.23439,0.0156 -0.23439,0.218751 0,0.0781 0.0625,0.125 0.14064,0.125 0.21875,0 0.75,-0.0312 0.96875,-0.0312 0.34375,0 0.73437,0.0312 1.0625,0.0312 0.0781,0 0.21875,0 0.21875,-0.23438 0,-0.0937 -0.0937,-0.109371 -0.17188,-0.109371 -0.26562,-0.0312 -0.5,-0.125 -0.5,-0.40625 0,-0.17188 0.0781,-0.29688 0.23438,-0.5625 l 0.90625,-1.51563 3.04687,0 c 0.0156,0.10938 0.0156,0.20313 0.0156,0.3125 0.0469,0.3125 0.1875,1.5625 0.1875,1.78125 0,0.359381 -0.60938,0.39063 -0.79688,0.39063 -0.14062,0 -0.26562,0 -0.26562,0.218751 0,0.125 0.10937,0.125 0.17188,0.125 0.20312,0 0.45312,-0.0312 0.65624,-0.0312 l 0.67188,0 c 0.73437,0 1.26562,0.0312 1.26562,0.0312 0.0937,0 0.21875,0 0.21875,-0.23438 0,-0.109371 -0.10937,-0.109371 -0.28125,-0.109371 -0.65624,0 -0.67187,-0.10938 -0.70312,-0.46875 l -0.73438,-7.45313 c -0.0312,-0.25 -0.0781,-0.26562 -0.20312,-0.26562 -0.125,0 -0.1875,0.0156 -0.29688,0.20312 l -4.1875,7 z m 1.43751,-1.84375 2.40625,-4.01562 0.40625,4.01562 -2.8125,0 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
-    <path
-       id="path11802"
-       d="m 142.21238,-67.366874 c 0.625,0 1.03126,0.45312 1.03126,1.29687 0,1 -0.56251,1.281251 -0.98438,1.281251 -0.4375,0 -1.04688,-0.156251 -1.32813,-0.578121 0.29688,0 0.5,-0.1875 0.5,-0.4375 0,-0.26563 -0.18749,-0.4375 -0.45312,-0.4375 -0.20313,0 -0.4375,0.125 -0.4375,0.45312 0,0.75 0.8125,1.250001 1.73437,1.250001 1.04688,0 1.79688,-0.73437 1.79688,-1.531251 0,-0.67187 -0.53125,-1.26562 -1.34375,-1.45312 0.625,-0.21875 1.10937,-0.75 1.10937,-1.39063 0,-0.64062 -0.71874,-1.09375 -1.54687,-1.09375 -0.85938,0 -1.5,0.45313 -1.5,1.0625 0,0.29688 0.1875,0.42188 0.40625,0.42188 0.25,0 0.40625,-0.17188 0.40625,-0.40625 0,-0.29688 -0.26563,-0.40625 -0.4375,-0.40625 0.34375,-0.4375 0.95313,-0.46875 1.09375,-0.46875 0.20312,0 0.8125,0.0625 0.8125,0.89062 0,0.54688 -0.23438,0.89063 -0.34375,1.01563 -0.23437,0.25 -0.42188,0.26562 -0.90625,0.29687 -0.15625,0 -0.21875,0.0156 -0.21875,0.125 0,0.10938 0.0781,0.10938 0.21875,0.10938 l 0.39062,0 z m 0,0"
-       style="fill:#000000;fill-opacity:1;stroke:none"
-       inkscape:connector-curvature="0" />
+     transform="translate(-149.00333,-103.25566)"
+     id="g3347">
+    <g
+       transform="translate(339.98099,124.938)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3231">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 5.671875,-4.859375 -1.125,-2.609375 C 4.703125,-7.75 5.0625,-7.8125 5.21875,-7.8125 c 0.0625,0 0.203125,-0.015625 0.203125,-0.21875 0,-0.125 -0.109375,-0.125 -0.1875,-0.125 -0.203125,0 -0.4375,0.015625 -0.640625,0.015625 l -0.703125,0 c -0.71875,0 -1.25,-0.015625 -1.265625,-0.015625 -0.09375,0 -0.203125,0 -0.203125,0.21875 0,0.125 0.09375,0.125 0.25,0.125 0.703125,0 0.75,0.109375 0.859375,0.40625 l 1.421875,3.3125 -2.59375,2.78125 C 1.9375,-0.84375 1.421875,-0.390625 0.53125,-0.34375 0.390625,-0.328125 0.296875,-0.328125 0.296875,-0.125 0.296875,-0.078125 0.3125,0 0.4375,0 0.609375,0 0.78125,-0.03125 0.953125,-0.03125 l 0.5625,0 C 1.90625,-0.03125 2.3125,0 2.6875,0 c 0.078125,0 0.234375,0 0.234375,-0.21875 0,-0.109375 -0.09375,-0.125 -0.15625,-0.125 -0.25,-0.03125 -0.40625,-0.15625 -0.40625,-0.34375 0,-0.203125 0.15625,-0.359375 0.5,-0.71875 l 1.0625,-1.15625 C 4.1875,-2.828125 4.8125,-3.53125 5.078125,-3.796875 l 1.25,2.953125 c 0.015625,0.015625 0.0625,0.140625 0.0625,0.15625 0,0.109375 -0.265625,0.3125 -0.640625,0.34375 -0.078125,0 -0.203125,0.015625 -0.203125,0.21875 C 5.546875,0 5.671875,0 5.71875,0 5.921875,0 6.171875,-0.03125 6.375,-0.03125 l 1.3125,0 C 7.90625,-0.03125 8.125,0 8.328125,0 c 0.09375,0 0.21875,0 0.21875,-0.234375 0,-0.109375 -0.125,-0.109375 -0.234375,-0.109375 C 7.609375,-0.359375 7.578125,-0.421875 7.375,-0.859375 L 5.796875,-4.5625 7.3125,-6.1875 c 0.125,-0.125 0.390625,-0.421875 0.5,-0.546875 0.515625,-0.53125 1,-1.015625 1.96875,-1.078125 0.109375,-0.015625 0.234375,-0.015625 0.234375,-0.21875 0,-0.125 -0.109375,-0.125 -0.15625,-0.125 -0.171875,0 -0.34375,0.015625 -0.515625,0.015625 l -0.546875,0 C 8.421875,-8.140625 8,-8.15625 7.625,-8.15625 c -0.078125,0 -0.21875,0 -0.21875,0.203125 0,0.125 0.078125,0.140625 0.140625,0.140625 0.203125,0.015625 0.40625,0.109375 0.40625,0.34375 L 7.9375,-7.453125 C 7.921875,-7.359375 7.90625,-7.25 7.765625,-7.09375 l -2.09375,2.234375 z m 0,0"
+         id="path3319" />
+    </g>
+    <g
+       transform="translate(349.69601,126.732)"
+       style="fill:#000000;fill-opacity:1"
+       id="use3235">
+      <path
+         inkscape:connector-curvature="0"
+         style="stroke:none"
+         d="m 2.015625,-2.65625 c 0.625,0 1.03125,0.453125 1.03125,1.296875 0,1 -0.5625,1.28125 -0.984375,1.28125 -0.4375,0 -1.046875,-0.15625 -1.328125,-0.578125 0.296875,0 0.5,-0.1875 0.5,-0.4375 0,-0.265625 -0.1875,-0.4375 -0.453125,-0.4375 -0.203125,0 -0.4375,0.125 -0.4375,0.453125 0,0.75 0.8125,1.25 1.734375,1.25 C 3.125,0.171875 3.875,-0.5625 3.875,-1.359375 3.875,-2.03125 3.34375,-2.625 2.53125,-2.8125 c 0.625,-0.21875 1.109375,-0.75 1.109375,-1.390625 0,-0.640625 -0.71875,-1.09375 -1.546875,-1.09375 -0.859375,0 -1.5,0.453125 -1.5,1.0625 0,0.296875 0.1875,0.421875 0.40625,0.421875 0.25,0 0.40625,-0.171875 0.40625,-0.40625 0,-0.296875 -0.265625,-0.40625 -0.4375,-0.40625 0.34375,-0.4375 0.953125,-0.46875 1.09375,-0.46875 0.203125,0 0.8125,0.0625 0.8125,0.890625 0,0.546875 -0.234375,0.890625 -0.34375,1.015625 -0.234375,0.25 -0.421875,0.265625 -0.90625,0.296875 -0.15625,0 -0.21875,0.015625 -0.21875,0.125 0,0.109375 0.078125,0.109375 0.21875,0.109375 l 0.390625,0 z m 0,0"
+         id="path3323" />
+    </g>
  </g>
 </svg>