$(\infty ,n)$-categories in context

Abstract

This note is a contribution written for the second volume of the Encyclopedia of mathematical physics. We give an informal introduction to the notions of an $(\infty ,n)$-category and $(\infty ,n)$-functor, discussing some of the different models that implement them. We also discuss the notions of a symmetric monoidal $(\infty ,n)$-category and symmetric monoidal $(\infty ,n)$-functor, recalling some important results whose statements employ the language of $(\infty ,n)$-categories.

Might differ slightly from published version