A morphism f:Y->X in a category is a monomorphism if, for any two morphisms u,v:Z->Y, fu=fv implies that u=v. In the categories of sets, groups, modules, etc., a monomorphism is the same as an injection, and is used synonymously with "injection" outside of category theory.

See also

Category, Epimorphism, Injection, Monomorph, Morphism

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Cite this as:

Weisstein, Eric W. "Monomorphism." From MathWorld--A Wolfram Web Resource.

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