(monomorphism)
11Epimorphism — In category theory an epimorphism (also called an epic morphism or an epi) is a morphism f : X rarr; Y which is right cancellative in the following sense: : g 1 o f = g 2 o f implies g 1 = g 2 for all morphisms g 1, g 2 : Y rarr; Z .Epimorphisms… …
12Kernel (category theory) — In category theory and its applications to other branches of mathematics, kernels are a generalization of the kernels of group homomorphisms and the kernels of module homomorphisms and certain other kernels from algebra. Intuitively, the kernel… …
13Abelian 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… …
14Normal morphism — In category theory and its applications to mathematics, a normal monomorphism or conormal epimorphism is a particularly well behaved type of morphism. A normal category is a category in which every monomorphism is normal. A conormal category is… …
15Regular category — In category theory, a regular category is a category with finite limits and coequalizers of kernel pairs, satisfying certain exactness conditions. In that way, regular categories recapture many properties of abelian categories, like the existence …
16Element (category theory) — In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows to restate definitions or properties of morphisms (such as… …
17Category (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 …
18Five lemma — In mathematics, especially homological algebra and other applications of Abelian category theory, the five lemma is an important and widely used lemma about commutative diagrams.The five lemma is valid not only for abelian categories but also… …
19Exact category — In mathematics, an exact category is a concept of category theory due to Daniel Quillen which is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and… …
20Ring homomorphism — In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication. More precisely, if R and S are rings, then a ring homomorphism is a function f : R → S such that …
