injective - Wiktionary, the free dictionary

From Wiktionary, the free dictionary

(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.

IPA^(key): /ɪnˈd͡ʒɛktɪv/
Rhymes: -ɛktɪv

injective (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); inverse-deterministic
Synonym: one-to-one
(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).