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 C C 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 † ∘ g R = 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) , f ∘ h = f ∘ k f \circ h = f \circ k and g ∘ h = g ∘ k g \circ h = g \circ k imply h = k h = 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 21:14:52.
See the history of this page for a list of all contributions to it.