epimorphism

In other words, f is the dual of an epimorphism.

It follows in particular that every cokernel is an epimorphism.

This term is also used in category theory to refer to any split epimorphism.

In this article, the term "epimorphism" will be used in the sense of category theory given above.

The composition of two epimorphisms is again an epimorphism.

An epimorphism (sometimes called a cover) is a surjective homomorphism.

It can be shown that a coequalizer q is an epimorphism in any category.

The companion terms epimorphism and monomorphism were first introduced by Bourbaki.

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

The converse, namely that every epimorphism be a coequalizer, is not true in all categories.

In a topos, every epimorphism is the coequalizer of its kernel pair.

This sequence may also be written without using special symbols for monomorphism and epimorphism:

For example, the inclusion map Q R, is a non-surjective epimorphism.

In many categories it is possible to write every morphism as the composition of a monomorphism followed by an epimorphism.

By the above, we know that for any such short exact sequence, f is a monomorphism and g is an epimorphism.

A regular epimorphism coequalizes some parallel pair of morphisms.

The induced epimorphism factors through both induced epimorphisms and .

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

Every retraction is an epimorphism, and every section is a monomorphism.

The placement of the 0's forces ƒ to be a monomorphism and g to be an epimorphism (see below).

A morphism that is both a monomorphism and an epimorphism is called a bimorphism.

Bourbaki uses epimorphism as shorthand for a surjective function.

Every surjective homomorphism is an epimorphism in Ring, but the converse is not true.

A conormal category is one in which every epimorphism is conormal.

A split epimorphism is an epimorphism having a right inverse.