Definitions for epimorphism
epi·mor·phism

WiktionaryRate this definition:0.0 / 0 votes

1. epimorphismnoun

   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 it's surjective

WikipediaRate this definition:0.0 / 0 votes

1. Epimorphism

   In category theory, an epimorphism (also called an epic morphism or, colloquially, an epi) is a morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms g1, g2: Y → Z, g 1 ∘ f = g 2 ∘ f ⟹ g 1 = g 2 . {\displaystyle g_{1}\circ f=g_{2}\circ f\implies g_{1}=g_{2}.} Epimorphisms are categorical analogues of onto or surjective functions (and in the category of sets the concept corresponds exactly to the surjective functions), but they may not exactly coincide in all contexts; for example, the inclusion Z → Q {\displaystyle \mathbb {Z} \to \mathbb {Q} } is a ring epimorphism. The dual of an epimorphism is a monomorphism (i.e. an epimorphism in a category C is a monomorphism in the dual category Cop). Many authors in abstract algebra and universal algebra define an epimorphism simply as an onto or surjective homomorphism. Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories. In this article, the term "epimorphism" will be used in the sense of category theory given above. For more on this, see § Terminology below.

WikidataRate this definition:4.0 / 1 vote

1. Epimorphism

   In category theory, an epimorphism is a morphism f : X → Y that is right-cancellative in the sense that, for all morphisms g1, g2 : Y → Z, Epimorphisms are analogues of surjective functions, but they are not exactly the same. The dual of an epimorphism is a monomorphism. Many authors in abstract algebra and universal algebra define an epimorphism simply as an onto or surjective homomorphism. Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories. In this article, the term "epimorphism" will be used in the sense of category theory given above. For more on this, see the section on Terminology below.

How to pronounce epimorphism?

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How to say epimorphism in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of epimorphism in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of epimorphism in Pythagorean Numerology is: 6

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Epimorphism
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Epimorphism
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=epimorphism