Definitions from Wiktionary (projective)

▸ adjective:  projecting outward
▸ adjective:  of, relating to, or caused by a projection
▸ adjective:  (geometry) Of or related to projective geometry:
▸ adjective:  (now usually in set phrases, of a property of a geometric object, figure, etc.) Invariant under projective transformations.
▸ adjective:  (of a geometric object, figure, etc.) Defined in or inhabiting a projective space.
▸ adjective:  (algebra) In a technical sense, general (but not necessarily so general as to be free); involving such objects:
▸ adjective:  (module theory, of a (left) module M over a ring R) 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).
▸ adjective:  (category theory, most generally, of an object P in a category) 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.
▸ adjective:  (group theory, of a profinite group G) Such that every epimorphism from a profinite group onto G has a right inverse which is a homomorphism.
▸ adjective:  (homological algebra, of a resolution) Such that every object in the resolution is projective.
▸ noun:  (psychology) An assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.
▸ noun:  (mathematics) A projective member of a category.
▸ noun:  (linguistics) A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.

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