nLab power 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

Definition

A power dagger 2-poset is a dagger 2-poset CC such that for every object AOb(C)A \in Ob(C) there exists an object 𝒫(A)\mathcal{P}(A) called the power object of AA and a morphism AHom C(A,𝒫(A))\in_A \in Hom_C(A, \mathcal{P}(A)) called subobject membership in AA, such that for each morphism RHom C(A,B)R \in Hom_C(A,B), there exists a map χ RMap C(A,P(B))\chi_R \in Map_C(A,P(B)) called the characteristic map such that R=( B )χ RR = (\in_B^\dagger) \circ \chi_R.

Examples

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

See also

Created on May 3, 2022 at 17:12:58. See the history of this page for a list of all contributions to it.