nLab
(1,0)-category

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

By the general rules of (n,r)(n,r)-categories, a (1,0)(1,0)-category is an \infty-category such that

  • any jj-morphism is an equivalence, for j>0j \gt 0;
  • any two parallel jj-morphisms are equivalent, for j>1j \gt 1.

You can start from any notion of \infty-category, strict or weak; up to equivalence, the result is always the same as a groupoid.

Revised on October 16, 2016 09:11:00 by Anonymous Coward (202.195.129.247)