injective

Etymology
This term was introduced by in his treatise Éléments de mathématique.

Adjective

 * 1)  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
 * 2)  Loosely, having a certain  generalizing property, abstracted from the study of $$\mathbb{Q}$$ as a $$\mathbb{Z}$$-module. Formally, such that any short exact sequence of (left) $$R$$-modules beginning with $$M$$ splits, or any of several equivalent statements: See.
 * 3)  Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism $$f:X \to Y$$ in $$C$$, for every morphism $$g:X \to Q$$ there exists a morphism $$h: Y \to Q$$ such that $$h \circ f = g$$; see.
 * 4)  Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
 * 1)  Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

Translations

 * Catalan: injectiu
 * Chinese:
 * Mandarin: 內射的, 单射的
 * Czech:, injektivní
 * Danish: injektiv
 * Finnish:
 * French:
 * German:
 * Greek: αμφιμονότιμη
 * Icelandic: eintækur
 * Irish: inteilgeach
 * Japanese: 入射の, 単射の
 * Polish: różnowartościowa
 * Portuguese: injetivo
 * Romanian: injectiv
 * Russian:
 * Spanish: inyectivo
 * Swedish: