Concept
Converse relation
Related concepts (24)
Reflexive relation
In mathematics, a binary relation R on a set X is reflexive if it relates every element of X to itself. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
Relation (mathematics)
In mathematics, a binary relation on a set may, or may not, hold between two given set members. For example, "is less than" is a relation on the set of natural numbers; it holds e.g. between 1 and 3 (denoted as 1
Dagger category
In , a branch of mathematics, a dagger category (also called involutive category or category with involution) is a equipped with a certain structure called dagger or involution. The name dagger category was coined by Peter Selinger. A dagger category is a category equipped with an involutive contravariant endofunctor which is the identity on . In detail, this means that: for all morphisms , there exist its adjoint for all morphisms , for all objects , for all and , Note that in the previous definition, the term "adjoint" is used in a way analogous to (and inspired by) the linear-algebraic sense, not in the category-theoretic sense.
Allegory (mathematics)
In the mathematical field of , an allegory is a that has some of the structure of the category Rel of sets and binary relations between them. Allegories can be used as an abstraction of categories of relations, and in this sense the theory of allegories is a generalization of relation algebra to relations between different sorts. Allegories are also useful in defining and investigating certain constructions in category theory, such as completions. In this article we adopt the convention that morphisms compose from right to left, so RS means "first do S, then do R".