• comma category

comma category (suomeksi)

Määritelmät:

• (lb, en, category theory) A category built on the basis of two other categories with a functor between them, whose objects are pairs ''object, morphism'' (''morphism, object'') where the ''object'' belongs to the first (second) category and the ''morphism'' to the second (first) category and the domain (codomain) of the ''morphism'' is the application of the functor to the ''object'', and whose morphisms are pairs ''morphism, commuting square'' (''commuting square, morphism'') formed by connecting two objects (as defined above) by means of three morphisms, one of them belonging to the first (second) category and the other two to the second (first) category, and the middle morphism being the application of the functor to the first (third) morphism.
• (lb, en, category theory) ''Most generally'': A category built on the basis of three other categories with a pair of functors from the flanking categories to the middle category; whose objects are triples ''object, morphism, object'' where the first and second ''objects'' belong to the first and third categories, respectively, and the ''morphism'' to the second category, and the domain of the ''morphism'' is the first functor applied to the first ''object'' and the codomain of the ''morphism'' is the second functor applied to the second ''object''; and whose morphisms are triples ''morphism, commuting square, morphism'' formed by connecting two objects (as defined above) by means of four morphisms, one belonging to the first category, a pair to the second category, and one to the third category, where the second morphism is the application of the first functor to the first morphism and the third morphism is the application of the second functor to the fourth morphism.