Given a dagger 2-poset$A$, the 2-poset of partial maps$Map_\bot(A)$ is the sub-2-poset whose objects are the objects of $A$ and whose morphisms are the partial maps of $A$.

Examples

For the dagger 2-poset of sets and relations $Rel$, the 2-poset of partial maps $Map_\bot(Rel)$ is equivalent to the category of sets and partial functions $Set_\bot$.