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Category of relations
From Wikipedia, the free encyclopedia
(Redirected from Category of sets and relations)
In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. The composition of two binary relations R: A → B and S: B → C is given by R o S(a, c) if for some b in B, R(a, b) and S(b, c).
Given any relation R(a, b), there is an adjoint relation R(b, a), defined in the obvious way. This makes Rel into a dagger category. A relation on a set (i.e. an endomorphism) is self-adjoint iff it is symmetric.
In fact, Rel is a dagger compact category.
