Injective
/ɪnˈd͡ʒɛktɪv/ adj
adj ·Rare ·Advanced level
Definitions
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 not-comparable
- 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 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 Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above). not-comparable
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.