Noun
(mathematics) an injective homomorphism
(biology) the absence of sexual dimorphism
(category theory) A morphism n such that for any other morphisms f and g, if
n
∘
f
=
n
∘
g
{\displaystyle n\circ f=n\circ g}
then f = g.
Hyponyms: equalizer, bimorphism, isomorphism, split monomorphism, global element
A strong epimorphism satisfies a certain lifting property with respect to commutative squares involving a monomorphism. Source: Internet
A regular monomorphism equalizes some parallel pair of morphisms. Source: Internet
For instance, since a function is bijective if and only if it is both injective and surjective, in abstract algebra a homomorphism is an isomorphism if and only if it is both a monomorphism and an epimorphism. Source: Internet
Every section is a monomorphism. Source: Internet
In an abelian category, every morphism f can be written as the composition of an epimorphism followed by a monomorphism. Source: Internet
In many categories it is possible to write every morphism as the composition of an epimorphism followed by a monomorphism. Source: Internet