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Mapping to and to yields a surjective group homomorphism. en.wikipedia.org

Many common notions from mathematics (e.g. surjective, injective, free object, basis, finite representation, isomorphism) are definable purely in category theoretic terms (cf. monomorphism, epimorphism). en.wikipedia.org

Many authors in abstract algebra and universal algebra define an epimorphism simply as an "onto" or surjective homomorphism. en.wikipedia.org

In some important cases, for example finite fields, is surjective. en.wikipedia.org

For in that case and its inverse preserve so must be surjective. en.wikipedia.org

A "subdirect product" is a subalgebra of the direct product such that all projection maps are surjective. en.wikipedia.org

They map the upper half-plane to itself (or to a real constant), but are not necessarily injective or surjective. en.wikipedia.org

The mapping is not surjective for all compact complex manifolds, but surjectivity does hold for all smooth projective varieties. en.wikipedia.org

The codomain affects whether a function is a surjection, in that the function is surjective if and only if its codomain equals its image. en.wikipedia.org

Likewise, a full functor need not be surjective on objects or morphisms. en.wikipedia.org

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