Category of relations

In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.

Category of Relations Rel.

Rel's opposite Rel^op.

A morphism (or arrow) R : A → B in this category is a relation between the sets A and B, so R ⊆ A × B.

The composition of two relations R: A → B and S: B → C is given by

(a, c) ∈ S o R ⇔ for some b ∈ B, (a, b) ∈ R and (b, c) ∈ S.

Rel has also been called the "category of correspondences of sets".

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