nLab tabular dagger 2-poset

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

Idea

A dagger 2-poset with tabulations, such as a tabular allegory.

Definition

A tabular dagger 2-poset is a dagger 2-poset CC such that for every object A:Ob(C)A:Ob(C) and B:Ob(C)B:Ob(C) and morphism R:Hom(A,B)R:Hom(A,B), there is an object |R|:Ob(C)\vert R \vert:Ob(C) and maps f:Hom(|R|,A)f:Hom(\vert R \vert, A), g:Hom(|R|,B)g:Hom(\vert R \vert, B), such that R=f gR = f^\dagger \circ g and for every object E:Ob(C)E:Ob(C) and maps h:Hom(E,|R|)h:Hom(E,\vert R \vert) and k:Hom(E,|R|)k:Hom(E,\vert R \vert), fh=fkf \circ h = f \circ k and gh=gkg \circ h = g \circ k imply h=kh = k.

Properties

The category of maps of a tabular dagger 2-poset has all pullbacks.

Examples

The dagger 2-poset Rel of sets and relations is a tabular dagger 2-poset.

See also

Created on May 3, 2022 at 17:14:52. See the history of this page for a list of all contributions to it.