# nLab unital dagger 2-poset

### Context

#### Higher category theory

higher category theory

## Definition

A unital dagger 2-poset is a dagger 2-poset $C$ with an object $\mathbb{1} \in Ob(C)$ such that for every morphism $f \in Hom(\mathbb{1}, \mathbb{1})$, $f \leq 1_\mathbb{1}$, and for every object $A \in Ob(C)$, there is an onto morphism $u_A \in Hom(A,\mathbb{1})$.

## Examples

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