(category theory) A category naturally associated to any monad T, and equivalent to the category of free T-algebras.

(category theory) An adjunction whose unit and counit are both natural isomorphisms.

(category theory) A category such that all of its objects form a set and all of its morphisms form a set.

(category theory) A category that is induced by a multidigraph thus: it has as its objects the vertices of the multidigraph and its morphisms are paths in the multidigraph; composition of morphisms is concatenation of paths, as long as the end of one path coincides with the beginning of the other path; an identity morphism of an object is an “empty path” at that vertex.

(category theory) A category whose morphisms are all identity morphisms.

Synonym of category mistake

plural of category error

(set theory) A fuzzy kind of category in which membership is determined not in binary (true-or-false) fashion but by a more general interval.

plural of Goguen category

plural of grammatical category