Commit 598b64ca authored by Leonard Guetta's avatar Leonard Guetta
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parent 02338bc4
\chapter{Homology and abelianization of \texorpdfstring{$\oo$}{ω}-categories}
\chaptermark{Homology of $\omega$-categories}
\section{Homology via the nerve}
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
All the results we have seen in this section are still true if we replace ``oplax'' by ``lax'' everywhere.
\section{Equivalences of \texorpdfstring{$\oo$}{ω}-categories and the folk model structure}
\section{Equivalences of \texorpdfstring{$\oo$}{ω}-categories and the folk model
\sectionmark{The folk model structure}
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:
......@@ -542,6 +542,7 @@ We now turn to the most important way of obtaining op\nbd{}prederivators.
reader can refer to any of the references on derivators previously cited.
\section{Morphisms of op-derivators, preservation of homotopy colimits}
\sectionmark{Morphisms of op-derivators}
We refer to \cite{leinster1998basic} for the precise definitions of
pseudo-natural transformation (called strong transformation there) and
......@@ -20,6 +20,11 @@
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......@@ -166,6 +171,10 @@ homotopy theory, polygraphs.
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