injective
Pronunciation: /ɪnˈd͡ʒɛktɪv/
The English word “injective” has 4 meanings listed here.
adjective
- 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
- 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.
- 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.
- Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
Etymology
Borrowed from French injectif.
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More English words
- injection molding
- injectional
- injectisome
- injectite
- injective function
- injectively
- injectiveness
- injectivity
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Definitions are from Wiktionary, extracted by Kaikki.org, and are available under the CC BY-SA 4.0 licence.