projective

The English word “projective” has 11 meanings listed here.

adjective

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.

noun

An assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.
A projective member of a category.
A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.

Etymology

Formed by the suffixation of prōiect- (the perfect passive participial stem of the Classical Latin prōiciō, whence the English verb project) with the English -ive, forming project + -ive; however, compare the post-Classical Latin prōiectīvus (“relating to purging”).

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Definitions are from Wiktionary, extracted by Kaikki.org, and are available under the CC BY-SA 4.0 licence.