Bachelor thesis about the Dold-Kan correspondence
https://github.com/Jaxan/Dold-Kan
You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
47 lines
1006 B
47 lines
1006 B
\documentclass[14pt]{beamer}
|
|
|
|
\usepackage[dutch]{babel}
|
|
|
|
\input{../thesis/preamble}
|
|
|
|
\title{Dold-Kan correspondentie}
|
|
\author{Joshua Moerman}
|
|
\institute[Radboud Universiteit Nijmegen]{Begeleid door Moritz Groth}
|
|
\date{}
|
|
|
|
\begin{document}
|
|
|
|
\begin{frame}
|
|
\titlepage
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
\frametitle{Dold-Kan Correspondentie}
|
|
\huge $$ \cat{Ch(Ab)} \simeq \cat{sAb} $$
|
|
\end{frame}
|
|
|
|
\section{Ketencomplex}
|
|
\begin{frame}
|
|
\frametitle{Ketencomplex}
|
|
\begin{definition}
|
|
Een \emph{ketencomplex} $C$ bestaat uit abelse groepen $C_n$ en homomorfismes $\del_n : C_{n+1} \to C_n$, zodat $\del_n \circ \del_{n+1} = 0$ voor alle $n \in \N$.
|
|
\end{definition}
|
|
\pause
|
|
\bigskip
|
|
Met andere woorden:
|
|
$$ \cdots \to C_4 \to C_3 \to C_2 \to C_1 \to C_0 $$
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
Uit $\del_n \circ \del_{n+1} = 0$ volgt $im(\del_{n+1}) \trianglelefteq ker(\del_n)$
|
|
\pause
|
|
Definieer: $H_n(C) = ker(\del_n) / im(\del_{n+1})$
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
\begin{center}
|
|
\Huge Vragen?
|
|
\end{center}
|
|
\end{frame}
|
|
|
|
\end{document}
|
|
|