From 8f41cc247e756d7c8a55c2bf397fba848f2808da Mon Sep 17 00:00:00 2001 From: Joshua Moerman Date: Mon, 10 Jun 2013 15:22:14 +0200 Subject: [PATCH] Thesis: titlepage/toc/... --- thesis/3_SimplicialAbelianGroups.tex | 2 +- thesis/DoldKan.tex | 40 +++++++++++++++++++++++++-- thesis/images/ru.pdf | Bin 0 -> 26101 bytes 3 files changed, 39 insertions(+), 3 deletions(-) create mode 100644 thesis/images/ru.pdf diff --git a/thesis/3_SimplicialAbelianGroups.tex b/thesis/3_SimplicialAbelianGroups.tex index 9bc345d..35b9a3e 100644 --- a/thesis/3_SimplicialAbelianGroups.tex +++ b/thesis/3_SimplicialAbelianGroups.tex @@ -224,7 +224,7 @@ As we are interested in simplicial abelian groups, it would be nice to make thes \subsection{The Yoneda lemma} Recall that the Yoneda lemma stated: $\mathbf{Nat}(y(C), F) \iso F(C)$, where $F:\cat{C}^{op} \to \Set$ is a functor and $C$ an object. In our case we consider functors $X: \DELTA^{op} \to \Set$ and objects $[n]$. So this gives us the natural bijection: $$ X_n \iso \Hom{\sSet}{\Delta[n]}{X}. $$ -So we can regard $n$-simplices in $X$ as maps from $\Delta[n]$ to $X$. This also extends to the abelian case, where we get an natural isomorphism (of abelian groups): +So we can regard $n$-simplices in $X$ as maps from $\Delta[n]$ to $X$. This also extends to the abelian case, where we get a natural isomorphism (of abelian groups): \begin{lemma}\emph{(The abelian Yoneda lemma)} Let $A$ be a simplicial abelian group. Then there is a group isomorphism $$ A_n \iso \Hom{\sAb}{\Z^\ast[\Delta[n]]}{A}, $$ diff --git a/thesis/DoldKan.tex b/thesis/DoldKan.tex index ff63180..7168392 100644 --- a/thesis/DoldKan.tex +++ b/thesis/DoldKan.tex @@ -1,4 +1,4 @@ -\documentclass[11pt]{amsproc} +\documentclass[titlepage, 11pt]{amsproc} % a la fullpage \usepackage{geometry} @@ -9,6 +9,9 @@ \usepackage[parfill]{parskip} \setlength{\marginparwidth}{2cm} +% toc/refs clickable +\usepackage{hyperref} + \theoremstyle{plain} \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} @@ -26,7 +29,40 @@ \author{Joshua Moerman} \begin{document} -\maketitle +\begin{titlepage} +\centering +\vspace{10cm} + +\includegraphics[scale=0.2]{ru}\\ +\textsc{Radboud University Nijmegen} +\vspace{3cm} + +{\huge \bfseries Dold-Kan Correspondence}\\ +Bachelor Thesis Mathematics +\vspace{3cm} + +\begin{minipage}{0.4\textwidth} +\begin{flushleft} \large +\emph{Author:}\\ +Joshua Moerman\\ +3009408 +\end{flushleft} +\end{minipage} +\begin{minipage}{0.4\textwidth} +\begin{flushright} \large +\emph{Supervisor:} \\ +Moritz Groth +\end{flushright} +\end{minipage} + +\vfill +\today + +\end{titlepage} + +\section*{Contents} +\renewcommand\contentsname{} +\tableofcontents \section*{Introduction} In this thesis we will look at a correspondence which was discovered by A. Dold \cite{dold} and D. Kan \cite{kan} independently, hence it is called the \emph{Dold-Kan correspondence}. 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