An conjunctive dagger 2-poset is a dagger 2-poset whose internal logic of the category of maps consists only of conjunction and true , or equivalently, whose category of maps has all pullback?s of monic maps.
Definition
An conjunctive dagger 2-poset is a dagger 2-poset such that
For each object , , with functionaldagger monomorphisms , , there is an object with functional dagger monomorphisms , , , such that and , and for every object with functional dagger monomorphisms , such that and , there is a functional dagger monomorphism such that .
Properties
For each object , the identity function is a functional dagger monomorphism, and for each object with a functional dagger monomorphism , .