A Boolean dagger 2-poset is a dagger 2-poset whose category of maps is an Boolean category?.

Definition

A Boolean dagger 2-poset$C$ is a Heyting dagger 2-poset where for each objects $A:Ob(C)$, $B:Ob(C)$ and monic map$i_{B,A}:Hom(B,A)$, there is a unitary isomorphism$j_{B,A}:A \cong^\dagger B \cup (B \Rightarrow 0)$.

Properties

The unitary isomorphism classes of monic maps into every object $A$ is a Boolean algebra?. Since every monic map is a map, the category of maps is a Boolean category?.

Examples

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