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monomorphisms

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Definitions of monomorphisms in various dictionaries:

MONOMORPHISMS - In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted wit...

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Plural form of monomorphism.

Monomorphisms might refer to
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 ↪ 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 f : X → Y such that, for all morphisms g1, g2 : Z → X,* * * * f * ∘ * * g * * 1 * * * = * f * ∘ * * g * * 2 * * * ⇒ * * g * * 1 * * * = * * g * * 2 * * * . * * * {\displaystyle f\circ g_{1}=f\circ g_{2}\Rightarrow g_{1}=g_{2}.} * 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 Cop. Every section is a monomorphism, and every retraction is an epimorphism.

Monomorphisms might refer to

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 ↪ 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 f : X → Y such that, for all morphisms g1, g2 : Z → X,*
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* {\displaystyle f\circ g_{1}=f\circ g_{2}\Rightarrow g_{1}=g_{2}.}
* 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 Cop. Every section is a monomorphism, and every retraction is an epimorphism.

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