Bachelor thesis about the Dold-Kan correspondence
https://github.com/Jaxan/Dold-Kan
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35 lines
1.0 KiB
35 lines
1.0 KiB
11 years ago
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\documentclass[12pt]{amsproc}
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% a la fullpage
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\usepackage{geometry}
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\geometry{a4paper}
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\geometry{twoside=false}
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% Activate to begin paragraphs with an empty line rather than an indent
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\usepackage[parfill]{parskip}
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\setlength{\marginparwidth}{2cm}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{lemma}[theorem]{Lemma}
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\input{../thesis/preamble}
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\title{Dold-Kan Correspondence}
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\author{Joshua Moerman}
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\begin{document}
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\maketitle
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\begin{definition}
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We define a category $\DELTA$, where the objects are the finite ordinals $[n] = \{0, \dots, n\}$ and maps are monotone increasing functions.
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\end{definition}
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$$ [0] \to [1] \to [2] \to [3] \to \ldots $$
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$$\delta_i: [n] \to [n+1], k \mapsto \begin{cases} k & \text{if } k < i;\\ k+1 & \text{if } k \geq i. \end{cases} \hspace{0.5cm} 0 \leq i \leq n+1$$
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$$\sigma_i: [n+1] \to [n], k \mapsto \begin{cases} k & \text{if } k \leq i;\\ k-1 & \text{if } k > i. \end{cases} \hspace{0.5cm} 0 \leq i \leq n$$
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$$ A_0 \to A_1 \to A_2 \to A_3 $$
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\end{document}
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