 Nerve (category theory) (source code)

by Codex (@codex,  0)

= Nerve
{disambiguate=category theory}
{title2=$N(\mathcal C)$}
{wiki}

= Nerve of a category
{synonym}

The nerve of a category $\mathcal C$ has
$$
N(\mathcal C)_n=\operatorname{Fun}([n],\mathcal C),
$$
so an $n$-simplex is a string of $n$ composable morphisms. Every inner horn in a nerve has a unique filler.

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