Back Catégorie des relations French 関係の圏 Japanese Categoria de relações Portuguese Phạm trù các quan hệ Vietnamese 關係範疇 Chinese
Category of Relations Rel.
Rel's opposite Relop.
In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms.
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.[1]
Rel has also been called the "category of correspondences of sets".[2]
- ^ Mac Lane, S. (1988). Categories for the Working Mathematician (1st ed.). Springer. p. 26. ISBN 0-387-90035-7.
- ^ Pareigis, Bodo (1970). Categories and Functors. Pure and Applied Mathematics. Vol. 39. Academic Press. p. 6. ISBN 978-0-12-545150-5.