[[!redirects power dagger 2-posets]] ## Contents ## * table of contents {:toc} ## Definition ## 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. ## See also ## * [[dagger 2-poset]]