nLab 2-poset of partial maps

Contents

Definition

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 functional morphisms of $A$.

Examples

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

See also

• partial map
• category of maps
• category of monic maps