category of modules

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• Category of vector spaces — In mathematics, especially category theory, the category K Vect has all vector spaces over a fixed field K as objects and K linear transformations as morphisms. If K is the field of real numbers, then the category is also known as Vec.Since… …   Wikipedia

• Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A …   Wikipedia

• Abelian category — In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of… …   Wikipedia

• Monoidal category — In mathematics, a monoidal category (or tensor category) is a category C equipped with a bifunctor ⊗ : C × C → C which is associative, up to a natural isomorphism, and an object I which is both a left and right identity for ⊗, again up to a… …   Wikipedia

• Complete category — In mathematics, a complete category is a category in which all small limits exist. That is, a category C is complete if every diagram F : J → C where J is small has a limit in C. Dually, a cocomplete category is one in which all small… …   Wikipedia

• Product (category theory) — In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… …   Wikipedia

• Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   Wikipedia

• Preadditive category — In mathematics, specifically in category theory, a preadditive category is a category that is enriched over the monoidal category of abelian groups. In other words, the category C is preadditive if every hom set Hom(A,B) in C has the structure of …   Wikipedia

• Functor category — In category theory, a branch of mathematics, the functors between two given categories can themselves be turned into a category; the morphisms in this functor category are natural transformations between functors. Functor categories are of… …   Wikipedia

• Yetter-Drinfeld category — In mathematics a Yetter Drinfel d category is aspecial type of braided monoidal category.It consists of modules over a Hopf algebra which satisfy some additionalaxioms. Definition Let H be a Hopf algebra over a field k . Let Delta denote the… …   Wikipedia

• Derived category — In mathematics, the derived category D(C) of an abelian category C is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on C. The construction proceeds on the… …   Wikipedia