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 entiredagger epimorphism$R:Hom(A,B)$ has a section.

Examples

The dagger 2-poset of choice sets and relations is an choice dagger 2-poset.