What is the meaning of Injective?
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 as a -module. Formally, such that any short exact sequence of (left) -modules beginning with splits, or any of several equivalent statements: See Injective module.
Loosely, having a property analogous to that which characterizes projective modules (see above). Formally, such that, given a monomorphism in , for every morphism there exists a morphism such that ; see Injective object.
Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above).
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