What is the meaning of Projective?

projecting outward

of, relating to, or caused by a projection

Of or related to projective geometry:

1. Invariant under projective transformations.
2. Defined in or inhabiting a projective space.

Invariant under projective transformations.

Defined in or inhabiting a projective space.

In a technical sense, general (but not necessarily so general as to be free); involving such objects:

1. Such that there is another (left) ${\displaystyle R}$-module ${\displaystyle N}$ with ${\displaystyle M\oplus N}$ a free ${\displaystyle R}$-module. Equivalently, projective in the category of modules (see below).
2. Such that, given an epimorphism ${\displaystyle e:E\to X}$ and morphism ${\displaystyle f:P\to X}$, ${\displaystyle f}$ factors through ${\displaystyle e}$; that is, there exists a morphism ${\displaystyle {\tilde {f}}:P\to E}$ with ${\displaystyle e\circ {\tilde {f}}=f}$.
3. Such that every epimorphism from a profinite group onto ${\displaystyle G}$ has a right inverse which is a homomorphism.
4. Such that every object in the resolution is projective.

Such that there is another (left) ${\displaystyle R}$-module ${\displaystyle N}$ with ${\displaystyle M\oplus N}$ a free ${\displaystyle R}$-module. Equivalently, projective in the category of modules (see below).

Such that, given an epimorphism ${\displaystyle e:E\to X}$ and morphism ${\displaystyle f:P\to X}$, ${\displaystyle f}$ factors through ${\displaystyle e}$; that is, there exists a morphism ${\displaystyle {\tilde {f}}:P\to E}$ with ${\displaystyle e\circ {\tilde {f}}=f}$.

Such that every epimorphism from a profinite group onto ${\displaystyle G}$ has a right inverse which is a homomorphism.

Such that every object in the resolution is projective.

An assessment test that presents subjects with some sort of stimulus to which they react by projecting or imagining details.

A projective member of a category.

A statement about a conditional or potential state of affairs, as opposed to one about a situation that actually exists or existed.

feminine singular of projectif

Source: wiktionary.org