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, MorphismExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Monomorphism." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Monomorphism.html