epimorphism

A morphism

e : A \to B

is an epimorphism if it is right-cancellative, i.e. if

f \circ e = g \circ e

for two morphisms

f,g : B \rightrightarrows T

then

f = g

In many concrete categories appearing in practice, these are a bit harder to understand than monomorphisms; in particular, epimorphisms usually are not to be confused with surjective structure-preserving maps. Stronger types of epimorphisms (such as regular epimorphisms) are often much better understood.

Dual monomorphism Related isomorphism, regular epimorphism External nLab link

Relevant implications

epimorphism andextremal monomorphism implies isomorphism
epimorphism andmonomorphism implies isomorphism
epimorphism andsplit monomorphism implies isomorphism
epimorphism implies extremal epimorphism
epimorphism implies isomorphism
epimorphism implies regular epimorphism
epimorphism implies strong epimorphism
extremal epimorphism implies epimorphism

Examples

There are 9 morphisms with this property.

Counterexamples

There are 6 morphisms without this property.

Unknown

There are 0 morphisms for which the database has no information on whether they satisfy this property.

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