A Boolean dagger 2-poset is a dagger 2-poset whose category of maps is an Boolean category?.
Definition
A Boolean dagger 2-poset is a Heyting dagger 2-poset where for each objects , and functional dagger monomorphism , there is a unitary isomorphismunitary isomorphism .
Properties
The unitary isomorphism classes of functional dagger monomorphisms into every object is a Boolean algebra?. Since every functional dagger monomorphism 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.