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

(category theory) A category in which every bimorphism is an isomorphism.

plural of balanced category

(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

plural of comma category

plural of coslice category

(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.

plural of Kleisli category