projective

Etymology
Formed by the suffixation of (the perfect passive participial stem of the Classical, whence the 🇨🇬 verb ) with the 🇨🇬, forming ; however, compare the post-Classical 🇨🇬.

Adjective
= f$$.
 * 1) projecting outward
 * of, relating to, or caused by a projection
 * 1)  Of or related to projective geometry:
 * 2)  Invariant under projective transformations.
 * 3)  Defined in or inhabiting a projective space.
 * 4)  In a technical sense, general (but not necessarily so general as to be free); involving such objects:
 * 5)  Such that there is another (left) $$R$$-module $$N$$ with $$M \oplus N$$ a free $$R$$-module. Equivalently, projective in the category of modules (see below).
 * 6)  Such that, given an epimorphism $$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
 * 1)  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 $$e \circ \tilde f
 * 1)  Such that every epimorphism from a profinite group onto $$G$$ has a right inverse which is a homomorphism.
 * 2)  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.
 * 2)  A projective member of a category.
 * 3)  A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
 * 1)  A projective member of a category.
 * 2)  A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
 * 1)  A projective member of a category.
 * 2)  A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
 * 1)  A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
 * 1)  A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.
 * 1)  A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.