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

TL;DR

This paper provides an informal introduction to $( , )$-categories and functors, discussing various models and their applications in mathematical physics, especially in symmetric monoidal contexts.

Contribution

It offers an accessible overview of $( , )$-categories, models, and their role in symmetric monoidal structures, highlighting key results in the field.

Findings

Different models of $( , )$-categories discussed

Important results involving $( , )$-categories summarized

Connections to symmetric monoidal structures explained

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.