# nLab power dagger 2-poset

### Context

#### Higher category theory

higher category theory

## Definition

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

## Examples

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