[[!redirects choice dagger 2-posets]] ## Contents ## * table of contents {:toc} ## Idea ## An choice dagger 2-poset is a dagger 2-poset whose [[category of maps]] satisfies the [[axiom of choice]] ## Definition ## An **choice dagger 2-poset** $C$ is a [[dagger 2-poset]] where for every object $A:Ob(C)$ and $B:Ob(C)$, every [[entire dagger morphism in a dagger 2-poset|entire]] [[dagger epimorphism in a dagger precategory|dagger epimorphism]] $R:Hom(A,B)$ has a section. ## Examples ## The dagger 2-poset of choice sets and relations is an choice dagger 2-poset. ## See also ## * [[dagger 2-poset]] * [[choice topical dagger 2-poset]]