A dagger 2-poset whose category of maps is a cartesian monoidal category?.
Definition
A cartesian dagger 2-poset is a unital dagger 2-poset such that for every object and , is a meet-semilattice with top morphism and meet operation , and there is an object such that there exist maps and such that and , for every onto morphism and .
Examples
The dagger 2-poset of sets and relations is a cartesian dagger 2-poset.