epimorphism

Noun

Meaning

epimorphism (plural epimorphisms)

(category theory) A morphism p such that for any other pair of morphisms f and g, if



f
∘
p
=
g
∘
p


{\displaystyle f\circ p=g\circ p}

, then f = g.

Synonyms

Related terms

Examples

Any morphism with a right inverse is an epimorphism, but the converse is not true in general. Source: Internet

A morphism f:A → B of rings is a homological epimorphism if it is an epimorphism and it induces a full and faithfull functor on derived categories: D(f) : D(B) → D(A). Source: Internet

A similar argument shows that the natural ring homomorphism from any commutative ring R to any one of its localizations is an epimorphism. Source: Internet

A strong epimorphism satisfies a certain lifting property with respect to commutative squares involving a monomorphism. Source: Internet

A split epimorphism is a morphism which has a right-sided inverse. Source: Internet

As some of the above examples show, the property of being an epimorphism is not determined by the morphism alone, but also by the category of context. Source: Internet

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