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 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.

(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 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 such that all of its objects form a set and all of its morphisms form a set.

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

(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 category error