injective
English
editEtymology
edit(This etymology is missing or incomplete. Please add to it, or discuss it at the Etymology scriptorium. Particularly: “cf. discussion page”) This term was introduced by Nicolas Bourbaki in his treatise Éléments de mathématique.
Pronunciation
editAdjective
editinjective (not comparable)
 (mathematics) Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inversedeterministic
 Synonym: onetoone
 (algebra, module theory, of a (left) module over a ring ) Loosely, having a certain generalizing property, abstracted from the study of as a module. Formally, such that any short exact sequence of (left) modules beginning with splits, or any of several equivalent statements: See Injective module.
 (category theory, most generally, of an object in a category ) Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism in , for every morphism there exists a morphism such that ; see Injective object.
 (homological algebra, of a resolution) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
Derived terms
editRelated terms
editTranslations
editinversedeterministic

See also
editFrench
editPronunciation
edit IPA^{(key)}: /ɛ̃.ʒɛk.tiv/
 Homophone: injectives
Adjective
editinjective
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