A power dagger 2-poset is a dagger 2-poset$C$ such that for every object $A:Ob(C)$ there exists an object $\mathcal{P}(A)$ called the power object of $A$ and a morphism $\in_A:Hom(A, \mathcal{P}(A))$ called subobject membership in $A$, such that for each morphism $R:Hom(A,B)$, there exists a morphism $\chi_R:(A,P(B))$ called the characteristic morphism such that $R = (\in_B^\dagger) \circ \chi_R$.

Examples

The dagger 2-poset of sets and relations is a power dagger 2-poset.