## Idea $Rel$ is the category of sets, with morphisms the relations between sets. ## Definition $Rel$ is a [[well-pointed dagger 2-poset|well-pointed]] [[locally Heyting-algebraic 2-poset|locally Heyting-algebraic]] [[power dagger 2-poset|power]] [[unital dagger 2-poset|unital]] [[tabular dagger 2-poset|tabular]] [[division dagger 2-poset|division]] [[semiadditive dagger 2-poset|semiadditive]] [[dagger 2-poset]] with an initial pointed unary system. ## See also * [[HilbR]]