injective

Fetched 2026-10-26 (cache).

Synonyms: invective, infective, objective, inventive, incentive, intentive, inactive, adjective, inductive, inceptive, ejective

Antonyms: invective, infective, objective, inventive, incentive, intentive, inactive, adjective, inductive, inceptive, ejective

Related words from Datamuse; suggestions, not definitions.

Adjective

1. {{lb|en|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
2. {{lb|en|algebra|[[module]] theory|of a (left) [[module]] <math>M</math> over a [[ring]] <math>R</math>}} Loosely, having a certain [[generalize| generalizing]] property, [[abstract|abstracted]] from the study of <math>\mathbb{Q}</math> as a <math>\mathbb{Z}</math>-module. Formally, such that any [[short exact sequence]] of (left) <math>R</math>-modules beginning with <math>M</math> [[split|splits]], or any of several equivalent statements: See {{w|Injective module}}.
3. {{lb|en|category theory|most generally|of an [[object]] <math>Q</math> in a [[category]] <math>C</math>}} Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a [[monomorphism]] <math>f:X \to Y</math> in <math>C</math>, for every [[morphism]] <math>g:X \to Q</math> there exists a morphism <math>h: Y \to Q</math> such that <math>h \circ f = g</math>; see {{w|Injective object}}.
4. {{lb|en|[[homological algebra]]|of a [[resolution]]}} Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).

Source: Wiktionary · CC BY-SA 4.0 (Wiktionary dump) · cached copy, not a rewrite.