preface.tex

\chapter{Preface}

The following text are my personal notes for the lecture course \emph{Foundations in Representation Theory}, also known as \emph{Homological Algebra}, that was held in the winter semester 2018/19 by Dr.\ Hans Franzen  at the University of Bonn.

The recommended literature are \cite{Working} and \cite{Schubert} for category theory, \cite[Chapter~1]{SheavesManifolds} and \cite{Weibel} for homological algebra, and \cite{Elements} for representation theory.
The author can also recommend \cite{BasicCategory} und \cite{Brandenburg} for category theory.

The numbering of these notes is consistent with the numbering from the lecture.
Additional remarks and statements that were not present in the lecture itself are marked with the symbol~\textsuperscript{\extrasymbol} and use their own distinct numbering.
Unnumbered remarks and statements were given the lecture, but outside of the usual numbering.

These notes are currently incomplete.
The following key points are currently missing:
\begin{itemize}
  \item
    The contents of the last two lectures.
  \item
    The proof of the snake lemma.
  \item
    The proof of the long exact cohomology sequence.
  \item
    The proof of the long exact sequence of the cone.
  \item
    A list of symbols.
\end{itemize}