Rune Haugseng
Invited contribution to the Encyclopedia of Mathematical Physics. We give an introduction to the homotopical theory of higher categories, focused on motivating the definitions of the basic objects, namely $\infty$-categories and $(\infty,n)$-categories.
This paper contains 18 sections, 4 theorems, 30 equations.
Proposition 2.3.2
A simplicial set $X$ is isomorphic to the nerve of a category if and only if every inner horn $\Lambda^{n}_{i} \if@display\longrightarrow \rightarrow X$ for $0 < i < n$ extends uniquely to an $n$-simplex, i.e. there is a unique way to fill in the diagram \begin{tikzcd} \Lambda^{n}_{i} \arrow{r
