nLab W-topical 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 W-topical dagger 2-poset is a dagger 2-poset whose category of maps is a W-topos.

Definition

A W-topical dagger 2-poset CC is an elementarily topical dagger 2-poset with an object Ob(C)\mathbb{N} \in Ob(C) and maps 0Map C(𝒫(0),𝒩)0 \in Map_C(\mathcal{P}(0),\mathcal{N}) and sMap C(,)s \in Map_C(\mathbb{N},\mathbb{N}), such that for every object AA with maps 0 AMap C(𝒫(0),A)0_A \in Map_C(\mathcal{P}(0),A) and s AMap C(A,A)s_A \in Map_C(A,A), there is a map fMap C(,A)f \in Map_C(\mathbb{N},A) such that f0=0 Af \circ 0 = 0_A and fs=s Aff \circ s = s_A \circ f.

Examples

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

See also

Created on May 3, 2022 at 17:20:51. See the history of this page for a list of all contributions to it.