nLab
(2,1)-category

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Context

2-Category theory

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

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)-categories, a (2,1)-category is an ∞-category such that

  • any j-morphism is an equivalence, for j>1;
  • any two parallel j-morphisms are equivalent, for j>2.

You can start from any notion of ∞-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)
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