\chapter{Homology and abelianization of \texorpdfstring{$\oo$}{ω}-categories}
\chaptermark{Homology of $\omega$-categories}
\section{Homology via the nerve}
\begin{paragr}
We denote by $\Ch$ the category of non-negatively graded chain complexes of abelian groups. Recall that $\Ch$ can be equipped with a cofibrantly generated model structure, known as the \emph{projective model structure on $\Ch$}, where:
@@ -526,7 +526,9 @@ From now on, we will consider that the category $\Psh{\Delta}$ is equipped with
\begin{remark}
All the results we have seen in this section are still true if we replace ``oplax'' by ``lax'' everywhere.
\end{remark}
\section{Equivalences of \texorpdfstring{$\oo$}{ω}-categories and the folk model structure}
\section{Equivalences of \texorpdfstring{$\oo$}{ω}-categories and the folk model
structure}
\sectionmark{The folk model structure}
\begin{paragr}\label{paragr:ooequivalence}
Let $C$ be an $\omega$-category. We define the equivalence relation $\sim_{\omega}$ on the set $C_n$ by co-induction on $n \in\mathbb{N}$. For $x, y \in C_n$, we have $x \sim_{\omega} y $ when: