Category Of Relations
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 R if (and only if) for some b ∈ B, (a, b) ∈ R and (b, c) ∈ S.
Read more about Category Of Relations: Properties
Famous quotes containing the words category of, category and/or relations:
“Despair is typical of those who do not understand the causes of evil, see no way out, and are incapable of struggle. The modern industrial proletariat does not belong to the category of such classes.”
—Vladimir Ilyich Lenin (1870–1924)
“I see no reason for calling my work poetry except that there is no other category in which to put it.”
—Marianne Moore (1887–1972)
“I only desire sincere relations with the worthiest of my acquaintance, that they may give me an opportunity once in a year to speak the truth.”
—Henry David Thoreau (1817–1862)