projective resolution

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• Resolution — may refer to: Resolution (audio), a measure of digital audio quality Resolution (logic), a rule of inference used for automated theorem proving Resolution (law), a written motion adopted by a deliberative body Resolution (debate), the statement… …   Wikipedia

• Projective module — In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… …   Wikipedia

• Projective cover — In 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. Definition Let mathcal{C} be a category and X an object in… …   Wikipedia

• Resolution (mathematics) — In mathematics, a resolution may mean:* a resolution in homological algebra, i.e. injective resolution, or projective resolution/free resolution * resolution of singularities, a fundamental issue of birational geometry, whether a birational… …   Wikipedia

• Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

• Koszul-Tate resolution — In mathematics, a Koszul Tate resolution or Koszul Tate complex is a projective resolution of R / M that is an R algebra (where R is a commutative ring and M is an ideal). They were introduced by John Tate and have been used to calculate BRST… …   Wikipedia

• Flat module — In abstract algebra, a flat module over a ring R is an R module M such that taking the tensor product over R with M preserves exact sequences.Vector spaces over a field are flat modules. Free modules, or more generally projective modules, are… …   Wikipedia

• Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   Wikipedia

• Derived functor — In mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. Contents 1 Motivation 2 Construction… …   Wikipedia

• Ext functor — In mathematics, the Ext functors of homological algebra are derived functors of Hom functors. They were first used in algebraic topology, but are common in many areas of mathematics. Definition and computation Let R be a ring and let mathrm{Mod}… …   Wikipedia

• Horseshoe lemma — In homological algebra, the horseshoe lemma, also called the simultaneous resolution theorem, is a statement relating resolutions of two objects A and A to resolutions ofextensions of A by A . It says that if an object A is an extension of A by A …   Wikipedia