nLab
flat resolution

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Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

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diagram chasing

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Idea

In homological algebra a flat resolution is a resolution of a chain complex by a complex of flat modules.

Revised on September 4, 2012 20:36:52 by Urs Schreiber (131.174.190.104)
Edit | Back in time (1 revision) | See changes | History | Views: Print | TeX | Source | Linked from: vector space, crossed complex, quasi-isomorphism, projective object, presentation axiom, internally projective object, A-infinity-category, Moore complex, 2-crossed module, Dold-Kan correspondence, dg-category, Categories and Sheaves, kernel, cokernel, additive category, abelian category, exact functor, homological algebra, chain complex, category with translation, derived category, triangulated category, homology, category of chain complexes, Quillen exact category, differential graded algebra, Grothendieck category, complex, injective object, differential graded coalgebra, double complex, satellite, additive functor, homological perturbation theory, exact sequence, element in an abelian category, flat module, differential forms on simplices, enhanced triangulated category, pretriangulated dg-category, twisted complex, Grothendieck spectral sequence, spectral sequence, Hochschild-Serre spectral sequence, snake lemma, model structure on chain complexes, chain homology and cohomology, monoidal Dold-Kan correspondence, de Rham theorem, injective hull, Eilenberg-Zilber theorem, homotopically injective object, free module, free object, five lemma, stable derivator, stable model category, An Introduction to Homological Algebra, Koszul complex, split exact sequence, projective module, universal coefficient theorem, Ext, Tor, homological algebra - contents, connecting homomorphism, chain homotopy, spectral sequence of a filtered complex, Eilenberg-Zilber map, singular homology, bounded chain complex, Betti number, Koszul-Tate resolution, delta-functor, contents of contents, Bridgeland stability condition, suspension of a chain complex, Bockstein homomorphism, 3x3 lemma, diagram chasing, Leray spectral sequence, relative homology, derived functor in homological algebra, syzygy, projective resolution, reduced homology, null homotopy, ordinary homology, interval object in chain complexes, projective presentation, Baer's criterion, tensor product of chain complexes, horseshoe lemma, associated graded object, filtered chain complex, chain map, Serre spectral sequence, simplicial homology, (infinity,1)-category of chain complexes, flat resolution, salamander lemma, compactly generated triangulated category, spectral sequence of a double complex, injective module, injective presentation, cellular homology, total complex, homotopy category of chain complexes, projective cover, free resolution, elliptic chain complex, long exact sequence in homology, four lemma, Lazard's criterion, projector, connective chain complex