Projective

English

Etymology

Formed by the suffixation of Template:M (the perfect passive participial stem of the Classical Template:Der, whence the Template:Cog verb Template:M) with the Template:Cog, forming Template:Af; however, compare the post-Classical Template:Cog.

Pronunciation

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Adjective

1. projecting outward
2. of, relating to, or caused by a projection
3. Template:Lb Of or related to projective geometry:
   1. Template:Lb Invariant under projective transformations.
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   2. Template:Lb Defined in or inhabiting a projective space.
4. Template:Lb In a technical sense, general (but not necessarily so general as to be free); involving such objects:
   1. Template:Lb Such that there is another (left) $R$-module $N$ with $M\oplus N$ a free $R$-module. Equivalently, projective in the category of modules (see below).
   2. Template:Lb Such that, given an epimorphism $e:E\to X$ and morphism $f:P\to X$, $f$ factors through $e$; that is, there exists a morphism $\tilde{f}:P\to E$ with $e\circ \tilde{f}=f$.
   3. Template:Lb Such that every epimorphism from a profinite group onto $G$ has a right inverse which is a homomorphism.
   4. Template:Lb Such that every object in the resolution is projective.

Noun

1. Template:Lb An assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.
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2. Template:Label A projective member of a category.
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3. Template:Label 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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Related terms

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French

Pronunciation

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Adjective

1. Template:Inflection of