(category theory) The category opposite to that of a slice category.

(category theory) A category built out of a pair of functors that have the same codomain.

(information science) A reference that specifies within some taxonomy or text typology one or more defined categories into which the referenced article, computer file etc. belongs.

plural of category reference

(category theory) A category 𝒞 with a bifunctor ⊗:𝒞⨯𝒞→𝒞 which may be called tensor product, an associativity isomorphism 𝛼_(A,B,C):(A⊗B)⊗C≃A⊗(B⊗C), an object I which may be called tensor unit, a left unit natural isomorphism 𝜆_A:I⊗A≃A, a right unit natural isomorphism 𝜌_A:A⊗I≃A, and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).

(cycling) The toughest category of climbs, tougher than category 1. One of six categories of climbs, HC, 1, 2, 3, 4, and not classified; not classified being the easiest.

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

(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.