morphism

Noun

Meaning

(mathematics, category theory) (formally) An arrow in a category; (less formally) an abstraction that generalises a map from one mathematical object to another and is structure-preserving in a way that depends on the branch of mathematics from which it arises.

(biology) Being or having distinct variants of a plant or animal species in the same locale; polymorphism.

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Phrases with the word

Examples

Any morphism with a right inverse is an epimorphism, but the converse is not true in general. Source: Internet

A groupoid is a category in which every morphism is an isomorphism. Source: Internet

A morphism f:A → B of rings is a homological epimorphism if it is an epimorphism and it induces a full and faithfull functor on derived categories: D(f) : D(B) → D(A). Source: Internet

Any preordered set (P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y. Between any two objects there can be at most one morphism. Source: Internet

Color morphism A melanistic jaguar is a color morph which occurs at about 6 percent frequency in populations. Source: Internet

Briefly, if we consider a morphism between two objects as a "process taking us from one object to another", then higher-dimensional categories allow us to profitably generalize this by considering "higher-dimensional processes". Source: Internet

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