- epimorphism
-
A map f such that whenever g composed with f equals h composed with f, then g=h. In most everyday categories, a map is an epimorphism iff its surjective
Wikipedia foundation.
epimorphism
Look at other dictionaries:
Epimorphism — 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… … Wikipedia
epimorphism — /ep euh mawr fiz euhm/, n. Math. a homomorphism that maps from one set onto a second set. [EPI + MORPHISM] * * * … Universalium
epimorphism — epi·mor·phism … English syllables
epimorphism — ˌepə̇ˈmȯrˌfizəm noun ( s) Etymology: epi (on) + homomorphism : an onto homomorphism * * * /ep euh mawr fiz euhm/, n. Math. a homomorphism that maps from one set onto a second set. [EPI + MORPHISM] … Useful english dictionary
Morphism — In mathematics, a morphism is an abstraction derived from structure preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear… … Wikipedia
Monomorphism — This page is about the mathematical term. For other uses, see Monomorphic (disambiguation) or Polymorphism (disambiguation). In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from … Wikipedia
Regular 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 … 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
Exact 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… … Wikipedia
Normal 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… … Wikipedia
