projective
Projecting outwardProjecting outward
Meaning
8 sensesProjecting outward
Of, relating to, or caused by a projection
Of or related to projective geometry:
(usually)Invariant under projective transformations.
(usually)Defined in or inhabiting a projective space.
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).
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.
Origin
Formed by the suffixation of prōiect- (the perfect passive participial stem of the ClassicFormed 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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Forms
more projective, most projective| Comparative | more projective Lesson |
|---|---|
| Superlative | most projective Lesson |
regular
Synonyms
14 synonymsWord family
8 related wordsLessons for this word
2 lessons- A2Comparatives — Because it has a comparative form
- A2Superlatives — Because it has a superlative form