Adds xymatrix diagrams

thesis/Makefile

@@ -1,10 +1,9 @@
 
-.PHONY: thesis fast images
+.PHONY: thesis fast images dirs
 
 # We don want to pollute the root dir, so we use a build dir
 # http://tex.stackexchange.com/questions/12686/how-do-i-run-bibtex-after-using-the-output-directory-flag-with-pdflatex-when-f
-thesis:
-	mkdir -p build
+thesis: dirs
 	cp references.bib build/
 	xelatex -file-line-error -output-directory=build thesis.tex
 	cd build; bibtex thesis
@@ -12,15 +11,18 @@ thesis:
 	xelatex -file-line-error -output-directory=build thesis.tex
 	cp build/thesis.pdf ./
 
-fast:
-	mkdir -p build
+fast: dirs
 	xelatex -file-line-error -output-directory=build thesis.tex
 	cp build/thesis.pdf ./
 
-images:
-	mkdir -p build
+images: dirs
 	xelatex -file-line-error -output-directory=build images.tex
 	xelatex -file-line-error -output-directory=build images.tex
 	scp build/images.pdf moerman@stitch.science.ru.nl:~/wvlt_images.pdf
 	ssh moerman@stitch.science.ru.nl 'pdf2svg wvlt_images.pdf wvlt_images.svg'
 	scp moerman@stitch.science.ru.nl:~/wvlt_images.svg ./images.svg
+
+dirs:
+	mkdir -p build
+	mkdir -p build/notes
+	mkdir -p build/diagrams

thesis/diagrams/Model_Cats_Pushouts.tex

@@ -0,0 +1,9 @@
+\xymatrix{
+	A \ar[r] \arcof[d]_{(\simeq)}^i & C \ar[d]^j \\
+	B \ar[r] & P
+}
+\qquad
+\xymatrix{
+	P \ar[r] \ar[d]^q & X \arfib[d]_{(\simeq)}^p \\
+	Z \ar[r] & Y
+}

thesis/diagrams/Model_Liftproblem.tex

@@ -0,0 +1,4 @@
+\xymatrix{
+	A \ar[d]^i \ar[r] & X \ar[d]^p \\
+	B \ar[r] & Y
+}

thesis/diagrams/Model_Replacements.tex

@@ -0,0 +1,9 @@
+\xymatrix{
+	\cat{0} \ar[rr] \arcof[dr] &                     & X \\
+	                           & X^{cof} \artfib[ur] &
+}
+\qquad
+\xymatrix{
+	X \ar[rr] \artcof[dr] &                    & \cat{1} \\
+	                      & X^{fib} \arfib[ur] &
+}

thesis/diagrams/Topr_No_Coequalizer.tex

@@ -0,0 +1,11 @@
+\xymatrixcolsep{7pc}
+\xymatrix{
+	\ast \ar@/^/[r]^{\ast \mapsto 0}
+	     \ar@/_/[r]_{\ast \mapsto 1} & I
+}
+\quad
+\xymatrixcolsep{7pc}
+\xymatrix{
+	I \ar@/^/[r]^{x \mapsto (x, sin(\pi x))}
+	  \ar@/_/[r]_{x \mapsto (x, -sin(\pi x))} & \R^2
+}

thesis/notes/Model_Categories.tex

@@ -19,20 +19,7 @@
 		\item[MC2] If $f$, $g$ and $fg$ are maps such that two of them are weak equivalences, then so it the third. This is called the \emph{2-out-of-3} property.
 		\item[MC3] All three classes of maps are closed under retracts\todo{Either draw the diagram or define a retract earlier}.
 		\item[MC4] In any commuting square as follows where $i \in \Cof$ and $p \in \Fib$,
-			\begin{center}
-			\begin{tikzpicture}
-			\matrix (m) [matrix of math nodes]{
-				A & X \\
-				B & Y \\
-			};
-
-			\path[->] (m-1-1) edge (m-1-2);
-			\path[->] (m-2-1) edge (m-2-2);
-			\path[->] (m-1-1) edge node[auto] {$i$} (m-2-1);
-			\path[->] (m-1-2) edge node[auto] {$p$} (m-2-2);
-
-			\end{tikzpicture}
-			\end{center}
+			\cdiagram{Model_Liftproblem}
 
 			there exist a lift $h: B \to Y$ if either 
 			\begin{itemize}
@@ -63,30 +50,7 @@
 
 Note that axiom [MC5a] allows us to replace any object $X$ with a weakly equivalent fibrant object $X^{fib}$ and by [MC5b] by a weakly equivalent cofibrant object $X^{cof}$, as seen in the following diagram:
 
-\begin{center}
-\begin{tikzpicture}
-\matrix (m) [matrix of math nodes]{
-	\cat{0} &         & X \\
-	        & X^{cof} &   \\
-};
-
-\path[->] (m-1-1) edge (m-1-3);
-\path[right hook->] (m-1-1) edge (m-2-2);
-\path[->>] (m-2-2) edge node[auto] {$ \simeq $} (m-1-3);
-
-\end{tikzpicture}\quad
-\begin{tikzpicture}
-\matrix (m) [matrix of math nodes]{
-	X &         & \cat{1} \\
-	  & X^{fib} &         \\
-};
-
-\path[->] (m-1-1) edge (m-1-3);
-\path[right hook->] (m-1-1) edge node[auto] {$ \simeq $} (m-2-2);
-\path[->>] (m-2-2) edge (m-1-3);
-
-\end{tikzpicture}
-\end{center}
+\cdiagram{Model_Replacements}
 
 The fourth axiom actually characterizes the classes of (trivial) fibrations and (trivial) cofibrations. We will abbreviate left lifting property with LLP and right lifting property with RLP. We will not prove these statements, but only expose them because we use them throughout this thesis. One can find proofs in \cite{dwyer, may}.
 
@@ -105,11 +69,11 @@ This means that once we choose weak equivalences and fibrations for a category $
 \Lemma{model-cats-pushouts}{
 	Let $\cat{C}$ be a model category. Consider the following two diagrams where $P$ is the pushout and pullback respectively.
 
-	\cimage{Model_Cats_Pushouts}
+	\cdiagram{Model_Cats_Pushouts}
 
 	\begin{itemize}
-		\item If $i$ is a (trivial) cofibrations, so is $j$.
-		\item If $p$ is a (trivial) fibrations, so is $q$.
+		\item If $i$ is a (trivial) cofibration, so is $j$.
+		\item If $p$ is a (trivial) fibration, so is $q$.
 	\end{itemize}
 }
 
@@ -146,8 +110,7 @@ In this thesis we often restrict to $1$-connected spaces. The full subcategory $
 \Lemma{topr-no-colimit}{
 	Let $r > 0$ and $\Top_r$ be the full subcategory of $r$-connected spaces. The diagrams
 
-	\cimage[scale=0.5]{Topr_No_Coequalizer}
-	\cimage[scale=0.5]{Topr_No_Equalizer}
+	\cdiagram{Topr_No_Coequalizer}
 
 	have no coequalizer and respectively no equalizer in $\Top_r$.
 }

thesis/preamble.tex

@@ -18,10 +18,14 @@
 % for multiple cites
 \usepackage{cite}
 
+% fancy diagrams
 \usepackage{tikz}
 \usetikzlibrary{matrix, arrows, decorations}
 \tikzset{node distance=2.5em, row sep=2.2em, column sep=2.7em, auto}
 
+% simple diagrams
+\usepackage[all,cmtip]{xy}
+
 \usepackage{graphicx}
 \graphicspath{ {./images/} }
 \usepackage{caption}
@@ -73,6 +77,12 @@
 \newcommand{\fib}{\twoheadrightarrow}	% fibration
 \newcommand{\we}{\tot{\simeq}}			% weak equivalence
 
+% for use in xy diagrams
+\newcommand{\arcof}{\ar@{^{(}->}}
+\newcommand{\artcof}{\ar@{^{(}->}|\simeq}
+\newcommand{\arfib}{\ar@{->>}}
+\newcommand{\artfib}{\ar@{->>}|\simeq}
+
 %\newcommand{\leftadj}{\ooalign{\hss\rightleftarrows\hss\cr\bot}}
 \newcommand{\leftadj}{\rightleftarrows}
 
@@ -167,4 +177,15 @@
 	\begin{center}
 	\includegraphics[#1]{#2}
 	\end{center}
-}
+}
+
+% simple way to center a diagram
+\newcommand{\cdiagrambase}[1]{
+	\begin{displaymath}
+	\input{#1}
+	\end{displaymath}
+}
+\newcommand{\cdiagram}[1]{
+	\cdiagrambase{diagrams/#1}
+}
+

thesis/test_diagram.sh

@@ -0,0 +1,8 @@
+#!/bin/bash
+set -e
+
+file=$1
+sed "s|__INPUT__|$file|" test_diagram.tex | xelatex -file-line-error -output-directory=build
+mv build/texput.pdf test_diagram.pdf
+exo-open test_diagram.pdf
+rm build/texput.*

thesis/test_diagram.tex

@@ -0,0 +1,14 @@
+\documentclass[a4paper, 12pt]{amsart}
+
+\input{style}
+\input{preamble}
+
+\begin{document}
+
+Your diagram:
+\cdiagrambase{__INPUT__}
+
+For reference, some default latex stuff:
+$$ A \cof B \we X \fib Y $$
+
+\end{document}