Relation Category

Def Relation Category Take sets as objects and take binary relations as morphisms, written as . That is, an morphism is a subset . And the identity morphism on a set is the identity relation:Given and , define composition byProp is indeed a category. Proof For all morphisms , and we have As is guaranteed by unital definition, we have Thus and similarly we have . Moreover, Indeed, And similarly Hence , the composition law is associative.