# 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 13, 2015 00:06:35 by John Dougherty (70.167.74.84)