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Fixes some latex issues wrt headings

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Joshua Moerman 11 years ago
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3 changed files with 5 additions and 5 deletions
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  1. 2
      thesis/notes/A_K_Quillen_Pair.tex
  2. 6
      thesis/preamble.tex
  3. 2
      thesis/thesis.tex

2
thesis/notes/A_K_Quillen_Pair.tex
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@ -1,5 +1,5 @@
\chapter{\texorpdfstring{$A$}{A} and \texorpdfstring{$K$}{K} form a Quillen pair} \chapter[A and K form a Quillen pair]{$A$ and $K$ form a Quillen pair}
\label{sec:a-k-quillen-pair} \label{sec:a-k-quillen-pair}
We will prove that $A$ preserves cofibrations and trivial cofibrations. We only have to check this fact for the generating (trivial) cofibrations in $\sSet$. Note that the contravariance of $A$ means that a (trivial) cofibrations should be sent to a (trivial) fibration. We will prove that $A$ preserves cofibrations and trivial cofibrations. We only have to check this fact for the generating (trivial) cofibrations in $\sSet$. Note that the contravariance of $A$ means that a (trivial) cofibrations should be sent to a (trivial) fibration.

6
thesis/preamble.tex
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@ -70,8 +70,8 @@
\newcommand{\dgAlg}[1]{\cat{dg\mbox{-}{#1}Alg}} % differential graded algebras over a ring \newcommand{\dgAlg}[1]{\cat{dg\mbox{-}{#1}Alg}} % differential graded algebras over a ring
\newcommand{\Ch}[1]{\cat{Ch_{n\geq0}({#1})}} % chain complexes \newcommand{\Ch}[1]{\cat{Ch_{n\geq0}({#1})}} % chain complexes
\newcommand{\CoCh}[1]{\cat{Ch^{n\geq0}({#1})}} % cochain complexes \newcommand{\CoCh}[1]{\cat{Ch^{n\geq0}({#1})}} % cochain complexes
\newcommand{\DGA}{\cat{DGA}} % cochain algebras \DeclareRobustCommand{\DGA}{\cat{DGA}} % cochain algebras
\newcommand{\CDGA}{\cat{CDGA}} % commutative cochain algebras \DeclareRobustCommand{\CDGA}{\cat{CDGA}} % commutative cochain algebras
\newcommand{\cof}{\hookrightarrow} % cofibration \newcommand{\cof}{\hookrightarrow} % cofibration
\newcommand{\fib}{\twoheadrightarrow} % fibration \newcommand{\fib}{\twoheadrightarrow} % fibration
@ -114,7 +114,7 @@
\renewcommand{\deg}[1]{{|{#1}|}} \renewcommand{\deg}[1]{{|{#1}|}}
\newcommand{\Char}[1]{char({#1})} \newcommand{\Char}[1]{char({#1})}
\newcommand{\RH}{\widetilde{H}} % reduced homology \newcommand{\RH}{\widetilde{H}} % reduced homology
\renewcommand{\C}{\mathcal{C}} % Serre mod C class \DeclareRobustCommand{\C}{\mathcal{C}} % Serre mod C class
\newcommand{\Apl}[0]{{A_{PL}}} % Apl simplicial set of polynomials \newcommand{\Apl}[0]{{A_{PL}}} % Apl simplicial set of polynomials
\newcommand{\titleCDGA}{\texorpdfstring{$\CDGA$}{CDGA}} \newcommand{\titleCDGA}{\texorpdfstring{$\CDGA$}{CDGA}}

2
thesis/thesis.tex
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@ -18,7 +18,7 @@
\part{Basics Of Rational Homotopy Theory} \part{Basics Of Rational Homotopy Theory}
\include{chapters/Basics_Of_Rational_Homotopy_Theory} \include{chapters/Basics_Of_Rational_Homotopy_Theory}
\part{CDGAs As Algebraic Models} \part{CDGA's As Algebraic Models}
\include{chapters/CDGA_As_Algebraic_Model_For_Rational_Homotopy_Theory} \include{chapters/CDGA_As_Algebraic_Model_For_Rational_Homotopy_Theory}
\part{Applications and Further Topics} \part{Applications and Further Topics}