projective
adjective C2- projecting outward
- of, relating to, or caused by a projection
- Invariant under projective transformations.
- Defined in or inhabiting a projective space.
- Such that there is another (left) R-module N with M⊕N a free R-module. Equivalently, projective in the category of modules (see below).
- Such that, given an epimorphism e:E→X and morphism f:P→X, f factors through e; that is, there exists a morphism ̃f:P→E with e∘̃f=f.
- Such that every epimorphism from a profinite group onto G has a right inverse which is a homomorphism.
- Such that every object in the resolution is projective.
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