Exact sequence
An exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category) such that the image of one morphism equals the k
Quasi-abelian category
In mathematics, specifically in category theory, a quasi-abelian category is a pre-abelian category in which the pushout of a kernel along arbitrary morphisms is again a kernel and, dually, the pullba
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 prototypical exampl
Pre-abelian category
In mathematics, specifically in category theory, a pre-abelian category is an additive category that has all kernels and cokernels. Spelled out in more detail, this means that a category C is pre-abel
Semi-abelian category
In mathematics, specifically in category theory, a semi-abelian category is a pre-abelian category in which the induced morphism is a bimorphism, i.e., a monomorphism and an epimorphism, for every mor
Mitchell's embedding theorem
Mitchell's embedding theorem, also known as the Freyd–Mitchell theorem or the full embedding theorem, is a result about abelian categories; it essentially states that these categories, while rather ab
In mathematics, specifically in category theory, an additive category is a preadditive category C admitting all finitary biproducts.