category of binary relations

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• Binary relation — Relation (mathematics) redirects here. For a more general notion of relation, see Finitary relation. For a more combinatorial viewpoint, see Theory of relations. In mathematics, a binary relation on a set A is a collection of ordered pairs of… …   Wikipedia

• Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A …   Wikipedia

• Category theory — In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them: it abstracts from sets and functions to objects and morphisms . Categories now appear in most branches of mathematics and in… …   Wikipedia

• 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 nowrap| R ⊆ A × B .The composition of two relations R …   Wikipedia

• Composition of relations — In mathematics, the composition of binary relations is a concept of forming a new relation S ∘ R from two given relations R and S, having as its most well known special case the composition of functions. Contents 1 Definition 2 Properties 3 J …   Wikipedia

• Allegory (category theory) — In mathematics, in the subject of category theory, an allegory is a category that has some of the structure of the category of sets and binary relations between them. Allegories can be used as an abstraction of categories of relations, and in… …   Wikipedia

• Theory of relations — This article is about the theory of relations with regard to its specifically combinatorial aspects. For a general discussion of the basic definitions, see Binary relation and Finitary relation. The theory of relations treats the subject matter… …   Wikipedia

• Regular category — In category theory, a regular category is a category with finite limits and coequalizers of kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence …   Wikipedia

• Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

• Monoid — This article is about the mathematical concept. For the alien creatures in the Doctor Who adventure, see The Ark (Doctor Who). Coherence law for monoid unit In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a… …   Wikipedia

• Order theory — For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… …   Wikipedia