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

Examples

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