Standard Lemma guide
Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.
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adj
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
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Topics: mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: one-to-one
Antonyms: none provided
adj
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: module theory
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
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.
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: most generally
Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
adj
Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
Definition source: English Wiktionary via Wiktextract
Usage: not-comparable
Qualifier: homological algebra
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
History
Borrowed from French injectif.
Across languages
20 source translations are retained for this English entry.
