nLab
(2,1)-category

Context

2-Category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

By the general rules of (n,r)(n,r)-categories, a (2,1)(2,1)-category is an \infty-category such that

  • any jj-morphism is an equivalence, for j>1j \gt 1;
  • any two parallel jj-morphisms are equivalent, for j>2j \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 22-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)