High Quality Content by WIKIPEDIA articles! In the theory of semigroups, a weak inverse of an element x in a semigroup (S, .) is an element y such that y.x.y = y. An element x of S for which there is an element y of S such that x.y.x = x is called regular. A regular semigroup is a semigroup in which every element is regular. If every element x in S has a unique inverse y in S in the sense that x.y.x = x and ...Täielik kirjeldus
High Quality Content by WIKIPEDIA articles! In the theory of semigroups, a weak inverse of an element x in a semigroup (S, .) is an element y such that y.x.y = y. An element x of S for which there is an element y of S such that x.y.x = x is called regular. A regular semigroup is a semigroup in which every element is regular. If every element x in S has a unique inverse y in S in the sense that x.y.x = x and y.x.y = y then S is called an inverse semigroup. In category theory, a weak inverse of an object A in a monoidal category C with monoidal product ¿ and unit object I is an object B such that both A¿B and B¿A are isomorphic to the unit object I of C. A monoidal category in which every morphism is invertible and every object has a weak inverse is called a 2-group.