nLab
(2,1)-category

Context

2-Category theory

Definitions

Transfors between 2-categories

Morphisms in 2-categories

Structures in 2-categories

Limits in 2-categories

Structures on 2-categories

Higher category theory

Basic concepts

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Basic theorems

  • -theorem
  • -theorem
  • -theorem

Applications

Models

    • /
    • /
    • = (n,n)-category
      • ,
    • =
      • =
      • =
    • = (n,0)-category
      • ,
  • /

Morphisms

Functors

Universal constructions

Extra properties and structure

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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

Last revised on May 13, 2015 at 00:06:35. See the history of this page for a list of all contributions to it.