What is "monomorphism"

n. 1 (context mathematics English) an injective homomorphism 2 (context biology English) the absence of sexual dimorphism 3 (context category theory English) A morphism ''n'' such that for any other morphisms ''f'' and ''g'', if $n\; circ\; f\; =\; n\; circ\; g$ then ''f'' = ''g''.

In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted with the notation $X \hookrightarrow Y$.

In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism, that is, an arrow such that, for all morphisms ,

Monomorphisms are a categorical generalization of injective functions (also called "one-to-one functions"); in some categories the notions coincide, but monomorphisms are more general, as in the examples below.

The categorical dual of a monomorphism is an epimorphism, i.e. a monomorphism in a category C is an epimorphism in the dual category C. Every section is a monomorphism, and every retraction is an epimorphism.