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Projective

adj, noun

Definitions

Adjective

1
projecting outward
2
of, relating to, or caused by a projection
3
Of or related to projective geometry:; Invariant under projective transformations. usually
"Hence the non-Euclidean angle is measured by one-half the logarithm of the cross-ratio of four rays. Although the Euclidean point of view has been adopted for simplicity, the final result, depending as it does only on the cross-ratio, is projective; it is therefore independent of the particular assumptions that the rays α and β are perpendicular and that the initial line bisects the angle between them."
4
Of or related to projective geometry:; Defined in or inhabiting a projective space. usually
5
In a technical sense, general (but not necessarily so general as to be free); involving such objects:; 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).

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6
In a technical sense, general (but not necessarily so general as to be free); involving such objects:; 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.
7
In a technical sense, general (but not necessarily so general as to be free); involving such objects:; Such that every epimorphism from a profinite group onto G has a right inverse which is a homomorphism.
8
In a technical sense, general (but not necessarily so general as to be free); involving such objects:; Such that every object in the resolution is projective.

Noun

1
An assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.
"The projectives suggested considerable difficulty with women and a conflict between sexual preoccupation and hostility."
2
A projective member of a category.
"By 2.2 we see that this is a full, contravariant imbedding, and by 2.3 the image of A in (A, G) is a generating set of small projectives."
3
A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
"There was no basis for expecting differences in the frequency of projectives or turnabouts as a function of partner."

Etymology

Etymology 1

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”).

Etymology 2

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