English

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An injective mapping

Etymology

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(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

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  • IPA(key): /ɪnˈd͡ʒɛktɪv/
  • Audio (US):(file)
  • Rhymes: -ɛktɪv

Adjective

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injective (not comparable)

  1. (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); inverse-deterministic
    Synonym: one-to-one
  2. (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.
  3. (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.
  4. (homological algebra, of a resolution) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

Derived terms

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Translations

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See also

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French

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Pronunciation

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Adjective

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injective

  1. feminine singular of injectif