
\newcommand{\titleCDGA}{\texorpdfstring{$\CDGA_\k$}{CDGA}}
\section{Homotopy theory of \titleCDGA}
\label{sec:model-of-cdga}

Recall the following facts about cdga's over a ring $\k$:
\begin{itemize}
	\item A map $f: A \to B$ in $\CDGA_\k$ is a \emph{quasi isomorphism} if it induces isomorphisms in cohomology.
	\item The finite coproduct in $\CDGA_\k$ is the (graded) tensor products.
	\item The finite product in $\CDGA_\k$ is the cartesian product (with pointwise operations).
	\item The equalizer (resp. coequalizer) of $f$ and $g$ is given by the kernel (resp. cokernel) of $f - g$. Together with the (co)products this defines pullbacks and pushouts.
	\item $\k$ and $0$ are the initial and final object.
\end{itemize}
In this chapter the ring $\k$ is assumed to be a field of characteristic zero.

\subsection{Cochain models for the $n$-disk and $n$-sphere}
\input{notes/CDGA_Basic_Examples}

\subsection{The Quillen model structure on \titleCDGA}
\input{notes/Model_Of_CDGA}

\subsection{Homotopy relations on \titleCDGA}
\input{notes/Homotopy_Relations_CDGA}
