nLab (2,1)-category

Context

2-Category theory

2-category theory

Structures on 2-categories

Higher category theory

higher category theory

Contents

Idea

By the general rules of $(n,r)$-categories, a $(2,1)$-category is an $\infty$-category such that * any $j$-morphism is an equivalence, for $j \gt 1$; * any two parallel $j$-morphisms are equivalent, for $j \gt 2$.

You can start from any notion of $\infty$-category, strict or weak; up to equivalence, the result can always be understood as a locally groupoidal $2$-category.

Models

So, a (2,1)-category is in particular modeled by

Revised on May 4, 2013 00:23:47 by Urs Schreiber (150.212.93.134)