In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.
The composition of two relations R: A → B and S: B → C is given by Rel has also been called the "category of correspondences of sets".
[note 1][3] A morphism in Rel is a relation, and the corresponding morphism in the opposite category to Rel has arrows reversed, so it is the converse relation.
[5] The category Rel was the prototype for the algebraic structure called an allegory by Peter J. Freyd and Andre Scedrov in 1990.
David Rydeheard and Rod Burstall consider Rel to have objects that are homogeneous relations.
[7] The same idea is advanced by Adamek, Herrlich and Strecker, where they designate the objects (A, R) and (B, S), set and relation.