Projective

Some articles on projective, projectives:

Projective Cover
... In the branch of abstract mathematics called category theory, a projective cover of an object X is in a sense the best approximation of X by a projective object P ... Projective covers are the dual of injective envelopes ...
Resolution (algebra) - Resolutions in Abelian Categories
... The analogous notion of projective and injective modules are projective and injective objects, and, accordingly, projective and injective resolutions ... If every object of A has a projective (resp ... injective) resolution, then A is said to have enough projectives (resp ...
Cartan–Eilenberg Resolution - Definition
... Let be an Abelian category with enough projectives, and let A∗ be a chain complex with objects in ... Ppq = 0 for q < 0) consisting of projective objects of and a chain map ε Pp0 → Ap such that Ap = 0 implies that the pth column is zero (Ppq = 0 for all q) ... and homology of the pth column of P∗∗ give projective resolutions of the pth boundary and homology groups of A∗, respectively ...
Schanuel's Lemma - Origins
... Kaplansky writes Early in the course I formed a one-step projective resolution of a module, and remarked that if the kernel was projective in one resolution it was projective in all ...
Abstract Algebraic Variety - Introduction and Definitions
... Next, one can define projective and quasi-projective varieties in a similar way ... definition of a variety is obtained by patching together smaller quasi-projective varieties ...