projective

adj, noun — 11 senses

projective

adj

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”).

8 senses
  1. 1projecting outward
  2. 2of, relating to, or caused by a projection
  3. 3Invariant under projective transformations.
  4. 4Defined in or inhabiting a projective space.
  5. 5Such that there is another (left) R-module N with M⊕N a…
  6. 6Such that, given an epimorphism e:E→X and morphism…
  7. 7Such that every epimorphism from a profinite group onto…
  8. 8Such that every object in the resolution is projective.
1

projecting outward

2

of, relating to, or caused by a projection

› Of or related to projective geometry:

3

Geometry, Mathematics, Sciences Usually Invariant under projective transformations.

Now usually in set phrases; figure; now usually in set phrases; figure Of a property of a geometric object

  • 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.1912 November 23, Edwin B. Wilson, Gillbert B. Lewis, “The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics”, in Proceedings of the American Academy of Arts and Sciences, volume 45, number 11, page 503:
4

Geometry, Mathematics, Sciences Usually, Of a geometric object Defined in or inhabiting a projective space.

› In a technical sense, general (but not…

5

Algebra, Mathematics, Sciences 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).

Of a (left) module M over a ring R

6

Algebra, Category theory, Computing, Engineering, Mathematics, Natural sciences, Physical sciences, Sciences 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.

Of an object P in a category

7

Algebra, Group theory, Mathematics, Sciences Of a profinite group G Such that every epimorphism from a profinite group onto G has a right inverse which is a homomorphism.

8

Algebra, Mathematics, Sciences Of a resolution Such that every object in the resolution is projective.

Homological algebra

Derived terms
complex projective line, projective basis, projective frame, projective resolution, projective variety, projectivise, projectivist, projectivity, projectivization, projectivize, quasi-projective, real projective plane

projective

noun

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”).

1

Human sciences, Psychology, Sciences 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.1984, Lawrence A. Pervin, Personality: Theory and Research, →ISBN, page 322:
  • For example, using projectives as a psychometric technique allows one to compare a person's score with those from a normative group, or with those from some relevant clinic group, or with some other clinically important criterion (e.g., response to treatment).2009, Paul J. Frick, Christopher T. Barry, Randy W. Kamphaus, Clinical Assessment of Child and Adolescent Personality and Behavior, →ISBN:
2 more examples
  • The unimpressive evidence for validity and operational problems related to projectives led Reilly and Chao to a pessimistic conclusion regarding projectives.2012, Linda C. Wing, Bernard R. Gifford, Policy Issues in Employment Testing, →ISBN, page 174:
  • With its origins based in the field of psychology, projectives (also referred to as projective exercises or projective techniques) when used in qualitative research are fun "assignments" most often implemented during focus groups. Their goal is to elicit deeper, more visceral feelings from respondents -- about brands, products, concepts, advertising, and so on -- viewpoints that may go unmentioned when using more direct lines of inquiry.2015, Paul Hackett, Qualitative Research Methods in Consumer Psychology, →ISBN:
2

Mathematics, Sciences 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.1965, Theory of Categories, →ISBN, page 109:
  • In particular our assumptions hold if B is an abelian category with enough projectives.1999, Maurice Auslander, Idun Reiten, Sverre O. Smalø, Selected Works of Maurice Auslander - Part 1, →ISBN, page 490:
1 more example
  • The idea behind “cheating with projectives” in a pre-Abelian category with a separating class of projectives is this: Make the arrows do the work that elements do in concrete categories.2012, M. Scott Osborne, Basic Homological Algebra, →ISBN, page 187:
3

Human sciences, Linguistics, Sciences 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.1995, Keith E. Nelson, Zita Reger, Children's Language - Volume 8, →ISBN:
  • The volitive moods (also called volitives, volitional forms, modals, or projectives) are the imperative, jussive, and cohortative.2007, Ronald James Williams, John C. Beckman, Williams' Hebrew Syntax, →ISBN, page 78:
1 more example
  • This implies they contain more information than projectives. For if language is a code, then every element of that code – here, every word, every form of a word – would register a distinct semantic ingredient.2012, Jean Curthoys, Victor Dudman, Victor Dudman's Grammar and Semantics, →ISBN, page 74:
Derived terms
41 termsbiprojective, multiprojective, nonprojective, preprojective, projective algebraic manifold, projective collineation, projective cone, projective correlation, projective differential geometry, projective frame, projective general linear group, projective general orthogonal group, projective general unitary group, projective geometry, projective Hilbert space, projective identification, projective limit, projective line, projective linear group, projectively, projective module, projective object, projective plane, projective plane dissection, projective representation, projective set, projective space, projective special linear group, projective special orthogonal group, projective special unitary group, projective symplectic group, projective test, projective texture mapping, projective transformation, projective unitary group, projective variety, projective vector field, projectivism, quasiprojective, semiprojective, superprojective
Related terms
projection

Entry derived from the Wiktionary, under licence CC BY-SA 4.0 — list of authors.