injective en · ADJ
Pronunciation
- /ɪnˈd͡ʒɛktɪv/
- (US) audio
Etymology
Borrowed from French injectif.
Meanings
- (not-comparable) 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
- (not-comparable, of a (left) module M over a ring R, qualifier:module theory) Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module.
- (not-comparable, of an object Q in a category C, qualifier:most generally) Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object.
- (not-comparable, of a resolution, qualifier:homological algebra) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
Deriveds
injective cogenerator · selfinjective · injective dimension · injective hull · injectivity · injective object · injectively · injective map · injective function · injective patch · injectiveness · injective sheaf · noninjective · injective module
Relateds
injectal · surjective · bijective
Synonyms
Translations (20)
ca injectiu (inverse-deterministic) · cmn 內射的 /内射的 (inverse-deterministic) · is eintækur (inverse-deterministic) · pt injetivo (inverse-deterministic) · es inyectivo (inverse-deterministic) · ja 入射の (inverse-deterministic) · ro injectiv (inverse-deterministic) · cs prostý (inverse-deterministic) · cs injektivní (inverse-deterministic) · ja 単射の (inverse-deterministic) · fr injectif (inverse-deterministic) · de injektiv (inverse-deterministic) · ga inteilgeach (inverse-deterministic) · sv injektiv (inverse-deterministic) · ru инъекти́вный (inverse-deterministic) · da injektiv (inverse-deterministic) · pl różnowartościowa (inverse-deterministic) · cmn 单射的 (inverse-deterministic) · fi injektiivinen (inverse-deterministic) · el αμφιμονότιμη (inverse-deterministic)