 Nerve (category theory)

The nerve of a category $\mathcal{C}$ hasso an $n$-simplex is a string of $n$ composable morphisms. Every inner horn in a nerve has a unique filler.

In category theory, the Nerve of a category is a construction that allows us to associate a simplicial set (or a simplicial object) with a given category. The Nerve captures the combinatorial structure of the category in a way that is useful for topological and homotopical applications.