nLab category of maps

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Definition

Given a dagger 2-poset AA, the category of maps Map(A)Map(A) is the sub-2-poset whose objects are the objects of AA and whose morphisms are the maps of AA. In every dagger 2-poset, given two maps f:Map A(a,b)f:Map_A(a,b) and g:Map A(a,b)g:Map_A(a,b), if fgf \leq g, then f=gf = g. This means that the sub-2-poset Map(A)Map(A) is a category and trivially a 2-poset.

Examples

  • For the dagger 2-poset Rel of sets and relations, the category of maps Map(Rel)Map(Rel) is equivalent to the category Set of sets and functions.

See also

Last revised on June 6, 2022 at 23:02:49. See the history of this page for a list of all contributions to it.