main.tex

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\input{config}

\includeonly
{
	introduction,
	ToposTheory,
	thefundamentalgroup,
	simplicialcomplexes,
	etalefunctor,
	isomorphism,
	outlook
}

\makeindex

\begin{document}

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	\vspace*{7em}
	\begin{center}
	{\large\bf R.A.C.H. Wols\par} \vspace{3em} {\LARGE\bf A McCord Functor for Alexandroff Categories\par} \vspace{3em} {\large\bf
	Master thesis\par} \vspace{1em} {\large\bf Thesis advisor:
	Dr. O.D. Biesel \par} \vspace{3em} {\large\bf July 7, 2016\\
	master exam: July 15, 2016\par}\vfill
	\includegraphics{ulzegel.pdf}\\
	\vspace{2em}
	{\large\bf Mathematisch Instituut, Universiteit Leiden}
	\end{center}


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	\begin{abstract}
	We shall generalize the construction of McCord's weak homotopy equivalence between the realization of the nerve of a finite poset and the original poset to Alexandroff categories and the induced toposes between them. For this, we shall construct a functor, called the McCord functor, which will give us the basis for a geometric morphism. Finally, we attempt to find sufficient conditions for flatness. The resulting geometric morphism will provide an equivalence of categories on the level of locally constant finite objects.
	\end{abstract}

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	{
		\raggedright
		{
			\Huge
			\itshape
				What I cannot create, \\
				I do not understand.
			\par
			\bigskip
		}
		\bigskip
		\bigskip
		\raggedleft
		\Large
		\MakeUppercase
		{
			Richard Feynman
		}
		\par
	}

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	\vfill

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	\addtocontents{toc}{\protect\enlargethispage{\baselineskip}}
	\tableofcontents
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	\pagenumbering{roman} 

	\include{introduction}

	\clearpage
	\pagenumbering{arabic} 

	\include{ToposTheory}
	\include{thefundamentalgroup}
	\include{simplicialcomplexes}
	\include{etalefunctor}
	\include{isomorphism}
	\include{outlook}

	\bibliographystyle{alpha}
	\bibliography{references}

	\printindex
	
\end{document}