diff --git a/presentation/presentation.tex b/presentation/presentation.tex index 609756c..fa71d53 100644 --- a/presentation/presentation.tex +++ b/presentation/presentation.tex @@ -1,4 +1,4 @@ -\documentclass{beamer} +\documentclass[14pt]{beamer} \usepackage[dutch]{babel} @@ -9,11 +9,14 @@ \usepackage{listings} \newcommand{\id}{\text{id}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\Z}{\mathbb{Z}} \newcommand{\cat}[1]{\mathbf{#1}} \newcommand{\eps}{\varepsilon} \newcommand{\I}{\,\mid\,} \newcommand{\then}{\Rightarrow} \newcommand{\inject}{\hookrightarrow} +\newcommand{\del}{\partial} \title{Dold-Kan correspondentie} \author{Joshua Moerman} @@ -26,23 +29,32 @@ \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} - $C_n \in \cat{Ab}$ + 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 -Enzoverder +\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 Questions? +\Huge Vragen? \end{center} \end{frame}