Definitions for monomorphism
monomor·phism

WiktionaryRate this definition:0.0 / 0 votes

1. monomorphismnoun

   an injective homomorphism

2. monomorphismnoun

   the absence of sexual dimorphism

WikipediaRate this definition:0.0 / 0 votes

1. 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 with the notation X ↪ Y {\displaystyle 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 f : X → Y such that for all objects Z and 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}\implies 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, that is, 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.

WikidataRate this definition:0.0 / 0 votes

1. 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 with the notation . In the more general setting of category theory, a monomorphism is a left-cancellative morphism, that is, an arrow f : X → Y such that, for all morphisms g1, g2 : Z → X, Monomorphisms are a categorical generalization of injective 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.

How to pronounce monomorphism?

1. Alex

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How to say monomorphism in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of monomorphism in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of monomorphism in Pythagorean Numerology is: 6

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Monomorphism
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Monomorphism
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=monomorphism