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 monic map , , there is an object with monic maps , , , such that and , and for every object with monic maps , such that and , there is a monic map such that .
Properties
For each object , the identity function is a monic map, and for each object with a monic map , .