Thesis: titlepage/toc/...
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@ -224,7 +224,7 @@ As we are interested in simplicial abelian groups, it would be nice to make thes
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\subsection{The Yoneda lemma}
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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:
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$$ X_n \iso \Hom{\sSet}{\Delta[n]}{X}. $$
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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):
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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):
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\begin{lemma}\emph{(The abelian Yoneda lemma)}
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Let $A$ be a simplicial abelian group. Then there is a group isomorphism
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$$ A_n \iso \Hom{\sAb}{\Z^\ast[\Delta[n]]}{A}, $$
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\documentclass[11pt]{amsproc}
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\documentclass[titlepage, 11pt]{amsproc}
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% a la fullpage
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\usepackage{geometry}
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\usepackage[parfill]{parskip}
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\setlength{\marginparwidth}{2cm}
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% toc/refs clickable
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\usepackage{hyperref}
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\theoremstyle{plain}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{proposition}[theorem]{Proposition}
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\author{Joshua Moerman}
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\begin{document}
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\maketitle
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\begin{titlepage}
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\centering
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\vspace{10cm}
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\includegraphics[scale=0.2]{ru}\\
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\textsc{Radboud University Nijmegen}
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\vspace{3cm}
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{\huge \bfseries Dold-Kan Correspondence}\\
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Bachelor Thesis Mathematics
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\vspace{3cm}
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\begin{minipage}{0.4\textwidth}
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\begin{flushleft} \large
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\emph{Author:}\\
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Joshua Moerman\\
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3009408
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\end{flushleft}
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\end{minipage}
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\begin{minipage}{0.4\textwidth}
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\begin{flushright} \large
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\emph{Supervisor:} \\
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Moritz Groth
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\end{flushright}
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\end{minipage}
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\vfill
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\today
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\end{titlepage}
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\section*{Contents}
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\renewcommand\contentsname{}
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\tableofcontents
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\section*{Introduction}
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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}. Abstractly it is the following equivalence of categories:
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