A morphism in a category is a monomorphism if, for any two morphisms , implies that . 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.

# Monomorphism

## See also

Category, Epimorphism, Injection, Monomorph, Morphism## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Monomorphism." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Monomorphism.html