nLab category of monic 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 monic maps MonoMap(A)MonoMap(A) is the sub-2-poset whose objects are the objects of AA and whose morphisms are the injective maps of AA.

In every dagger 2-poset, given two injective maps f:hom A(a,b)f:hom_A(a,b) and g:hom A(a,b)g:hom_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 monic maps MonoMap(Rel)MonoMap(Rel) is equivalent to the category of sets and injections.

See also

category: category theory

Last revised on June 7, 2022 at 02:52:19. See the history of this page for a list of all contributions to it.