[[!redirects unital dagger 2-posets]] ## Contents ## * table of contents {:toc} ## Definition ## 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 a morphism $u:A \to \mathbb{1}$ such that $1_A \leq u \circ u^\dagger$. ## Examples ## The dagger 2-poset of sets and relations is a unital dagger 2-poset. ## See also ## * [[dagger 2-poset]] * [[well-pointed dagger 2-poset]]