Tag: homological-algebra

101 Spectral sequences: opening the black box slowly with an example 2010-11-06T06:33:59.420

72 Algorithm or theory of diagram chasing 2009-12-28T02:34:26.017

60 Derived Functors Versus Spectral Sequences 2012-03-21T02:37:02.493

58 whence commutative diagrams? 2011-03-24T18:24:38.700

51 What is Homology anyway? 2017-07-23T11:43:55.147

50 Where do all these projection formulas come from? 2011-06-08T09:40:26.857

48 Why are spectral sequences so ubiquitous? 2009-12-07T00:43:37.563

44 What is Koszul duality? 2009-10-11T23:41:10.407

44 What is a cohomology theory (seriously)? 2009-11-19T16:26:06.903

43 How to make Ext and Tor constructive? 2011-01-03T00:09:40.540

40 Homological Algebra texts 2009-10-25T23:37:37.173

40 What the heck is the Continuum Hypothesis doing in Weibel's Homological Algebra? 2011-06-21T21:14:49.823

39 When are there enough projective sheaves on a space X? 2009-11-13T15:48:20.647

38 Kunneth formula for sheaf cohomology of varieties 2010-08-05T19:03:05.907

35 Do all exact $1 \to A \to A \times B \to B \to 1$ split for finite groups? 2011-11-04T03:26:41.060

35 A three-line proof of global class field theory? 2016-09-10T00:38:53.860

34 Chain homotopy: Why du+ud and not du+vd? 2009-12-15T11:12:19.120

34 Definition of an E-infinity algebra 2010-08-23T13:20:53.233

34 Motivating the category of chain complexes 2011-06-21T04:26:36.227

33 Heuristic explanation of why we lose projectives in sheaves. 2009-11-30T23:55:55.933

32 Why does non-abelian group cohomology exist? 2009-10-24T23:28:45.120

32 A down-to-earth introduction to the uses of derived categories 2010-09-21T14:51:01.377

31 How to think about model categories? 2009-10-23T21:00:31.737

31 Example Wanted: When Does Cech Cohomology Fail to be the same as Derived Functor Cohomology? 2010-03-25T14:48:13.970

31 introductory book on spectral sequences 2010-04-22T14:13:44.777

30 How do I know the derived category is NOT abelian? 2010-02-18T02:27:19.303

30 What is so "spectral" about spectral sequences? 2010-03-07T04:35:28.733

30 Categories First Or Categories Last In Basic Algebra? 2010-10-04T20:12:57.810

30 Non-split extension of the rationals by the integers 2012-08-22T21:02:15.993

30 A more natural proof of Dold-Kan? 2015-02-07T14:42:46.730

28 What was the error in the proof of Roos' theorem? 2018-01-20T22:27:48.457

26 Serre intersection formula and derived algebraic geometry? 2010-01-18T21:16:16.997

26 Poincare duality and the $A_\infty$ structure on cohomology 2010-12-23T11:32:48.923

25 triangulated vs. dg/A-infinity 2009-10-17T00:21:51.583

25 Some intuition behind the five lemma? 2009-10-26T22:23:23.453

25 Complete the following sequence: point, triangle, octahedron, . . . in a dg-category 2016-04-17T21:33:26.763

24 tips on cohomology for number theory 2009-12-11T20:12:59.703

24 Noncommutative rational homotopy type 2009-12-17T01:59:42.367

24 References for sign conventions in homological algebra 2011-01-26T04:22:35.093

24 origin of spectral sequences in algebraic topology 2014-01-31T13:36:52.137

23 Freyd-Mitchell's embedding theorem 2010-11-30T02:09:22.947

23 "Sums-compact" objects = f.g. objects in categories of modules? 2011-03-23T10:39:29.673

23 Does the Tate construction (defined with direct sums) have a derived interpretation? 2016-03-26T20:01:27.310

22 Is there an infinity × infinity lemma for abelian categories? 2009-11-07T21:47:45.547

22 Sums of injective modules, products of projective modules? 2009-11-30T14:47:52.983

22 History of Koszul complex 2013-10-30T01:55:32.903

22 Derived functors - homotopical vs homological approach 2015-06-05T10:50:51.590

21 Do DG-algebras have any sensible notion of integral closure? 2009-12-04T13:47:02.767

21 A Peculiar Model Structure on Simplicial Sets? 2010-02-05T13:53:15.303

21 Flat Module and Torsion-Free Module 2011-01-04T09:00:09.010

21 Why not define triangulated categories using a mapping cone functor? 2011-03-09T02:08:08.537

21 Homology theory constructed in a homotopy-invariant way 2011-10-18T12:33:32.340

21 (co)homology of symmetric groups 2014-09-11T14:58:35.027

20 Yoga of six functors for group representations? 2016-12-27T21:48:55.623

20 Example of an additive functor admitting no right derived functor 2017-03-20T11:18:06.930

20 About the abelian category of endofunctors of $\mathsf{Vect}$ 2017-05-16T20:20:18.170

19 Homological Algebra for Commutative Monoids? 2009-10-13T16:23:02.830

19 Homological algebra and calculus (as in Newton) 2009-10-15T20:36:46.077

19 A proof of the salamander lemma without Mitchell's embedding theorem? 2009-11-25T01:33:14.487

19 Homotopy flat DG-modules 2010-09-26T16:53:57.713

19 Is there an additive functor between abelian categories which isn't exact in the middle? 2010-11-14T05:08:42.567

19 Non-vanishing of group cohomology in sufficiently high degree 2011-05-11T20:12:23.123

19 Calculating Mayer-Vietoris efficiently 2012-03-15T00:51:37.270

18 distinguished triangles and cohomology 2009-10-31T09:47:40.333

18 A ring such that all projectives are stably free but not all projectives are free? 2010-06-08T04:08:38.100

18 Acyclic models via model categories? 2011-09-22T20:02:40.250

18 A spectral sequence for computing cohomology of a space from that of its strata 2016-03-07T22:56:46.177

17 Other examples of computations using transfer of structure from the chains to the homology? 2010-06-22T11:47:53.847

17 Singular Homology/Cohomology as a derived functor? 2011-05-29T22:32:52.737

17 Is homology finitely generated as an algebra? 2014-10-03T03:24:28.203

17 Is such a map null-homotopic? 2014-10-25T15:17:51.560

16 elementary Ext^1 intuition 2009-10-25T23:30:44.917

16 When does direct image with proper support have a right adjoint? 2009-10-29T18:38:08.370

16 Cohomology of associative algebras 2009-11-19T21:36:37.757

16 Idea of presheaf cohomology vs. sheaf cohomology 2010-07-05T11:12:55.913

16 how to make the category of chain complexes into an $\infty$-category 2012-04-13T15:57:10.490

16 Homology in the $A_\infty$ World 2013-03-26T19:03:00.780

16 Epimorphisms $\mathbb{Z}^{\mathbb{N}} \to \mathbb{Z}^{\mathbb{N}}$ are split 2013-08-15T09:01:52.903

16 Bar construction vs. twisted tensor product 2013-11-11T21:17:59.423

16 Are dualizable modules finitely generated? 2014-05-08T21:32:00.987

16 Grothendieck spectral sequence when one of the functors is contravariant 2015-12-27T00:37:37.133

16 Two points of view about Borel-moore homology 2016-09-08T11:44:17.537

15 Can we categorify the equation (1 - t)(1 + t + t^2 + ...) = 1? 2009-10-20T18:21:52.577

15 Equivalence of ordered and unordered cech cohomology. 2009-12-29T19:35:52.707

15 Does homology detect chain homotopy equivalence? 2010-01-06T22:05:33.697

15 Essential theorems in group (co)homology 2010-01-21T13:46:26.537

15 Mittag-Leffler condition: what's the origin of its name? 2010-02-09T00:21:37.567

15 Grothendieck's Tohoku Paper and Combinatorial Topology 2010-03-21T02:32:17.490

15 Comodule exercises desired 2010-07-28T19:58:26.780

15 abelian categories enriched over sheaves 2010-09-07T21:46:23.247

15 Tropical homological algebra 2011-02-10T11:18:25.490

15 When is a quasi-isomorphism necessarily a homotopy equivalence? 2011-03-24T05:46:49.047

15 Morita equivalence of DG algebras? (reference needed) 2011-12-11T17:28:09.290

15 Cov. right-exact additive functors that don't commute with direct sums? 2012-04-10T23:37:21.703

15 Characterising categories of vector spaces 2013-01-07T06:08:26.523

15 What is the purpose of section 3 of BBD? 2013-04-11T19:05:48.067

15 Lifting DG-categories to characteristic zero 2015-02-11T03:01:06.807

15 Homotopy transfer in the opposite direction 2015-05-18T14:29:28.290

15 Moduli space of boundary maps with prescribed chain and homology groups? 2015-09-16T15:57:11.117