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monomorphism
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Definitions of monomorphism in various dictionaries:
MONOMORPHISM - 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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an injective homomorphism |
the absence of sexual dimorphism |
Monomorphism description |
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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 gene |