Given a dagger 2-poset , the category of maps is the sub-2-poset whose objects are the objects of and whose morphisms are the maps of . In every dagger 2-poset, given two maps and , if , then . This means that the sub-2-poset is a category and trivially a 2-poset.
Examples
For the dagger 2-poset Rel of sets and relations, the category of maps is equivalent to the category Set of sets and functions.