A W-topical dagger 2-poset is a dagger 2-poset whose category of maps is a W-topos?.
Definition
A W-topical dagger 2-poset is an elementarily topical dagger 2-poset with an object and maps and , such that for every object with maps and , there is a map such that and .
Examples
The dagger 2-poset of sets and relations is a W-topical dagger 2-poset.