adj ·Rare ·Advanced level

Definitions

Adjective

1. 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 not-comparable
2. 2
   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
3. 3
   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
4. 4
   Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above). not-comparable

Synonyms

All synonyms

one to oneone-to-one

Example

More examples

"In algebra a monomorphism is an injective homomorphism."

Etymology

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

Related phrases

injective cogeneratorinjective dimensioninjective functioninjective hullinjective mapinjective moduleinjective objectinjective patchinjective sheaf

Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.