plural of category mistake

(category theory) A category whose objects are morphisms (of some given category) with a common codomain, and whose morphisms are commuting triangles where two morphisms of each of such triangles share the said common codomain.

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

(category theory) A category whose objects are functors (from some fixed given domain category to some fixed given codomain category) and whose morphisms are natural transformations.

(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).

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