76 Is there a sheaf theoretical characterization of a differentiable manifold? 2012-02-10T00:30:13.483

71 What is sheaf cohomology intuitively? 2010-09-16T12:39:18.877

70 equivalence of Grothendieck-style versus Cech-style sheaf cohomology 2009-11-05T04:47:03.340

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

44 What does a projective resolution mean geometrically? 2009-10-23T16:52:26.897

43 What are the benefits of viewing a sheaf from the "espace étalé" perspective? 2012-05-07T21:01:24.230

40 Is there a good way to think of vanishing cycles and nearby cycles? 2009-10-21T05:26:03.130

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

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

31 What is the inverse image sheaf necessary for in algebraic geometry? 2010-09-30T15:42:46.143

28 How should one think about sheafification and the difference between a sheaf and a presheaf 2010-11-07T21:12:30.197

27 What is the right version of "partitions of unity implies vanishing sheaf cohomology" 2010-01-12T17:48:42.377

25 Sheaf Description of G-Bundles 2009-10-25T02:52:32.917

24 What (if anything) happened to Intersection Homology? 2009-11-26T06:04:41.807

24 What is the Zariski topology good/bad for? 2010-04-15T20:32:47.687

23 Loop Spaces as Generalized Smooth spaces or as Infinite dimensional Manifolds? 2010-01-22T16:13:03.287

23 Why are quasitopological spaces needed in sheaf theoretic approaches to the h-principle? 2013-03-15T13:47:35.367

21 How do I compare the different notions of Fourier transform for sheaves? 2009-10-28T20:49:59.897

21 Naive question about constructing constructible sheaves. 2011-02-01T23:47:50.847

21 The topologies for which a presheaf is a sheaf? 2014-04-13T17:44:43.973

20 Applications of the "other" definition of Sheaves 2009-11-22T19:22:28.210

20 Galois Group as a Sheaf 2010-06-30T10:35:36.503

20 Why there is a Quot-scheme, not a Sub-scheme? 2016-11-07T09:31:48.033

19 Is there a "categorical" description of Grothendieck's algebra of differential operators? 2010-03-14T19:53:12.627

18 What is an example of a presheaf P where P^+ is not a sheaf, only a separated presheaf? 2009-10-15T17:12:18.250

18 Stacks and sheaves 2010-02-03T01:48:47.967

18 De Rham decomposition theorem, generalisations and good references 2010-06-13T16:38:54.043

18 Do I know what "coherent sheaf" means if I know what it means on locally Noetherian schemes? 2015-05-08T17:01:42.403

17 When will the pushforward of a structure sheaf still be a structure sheaf? 2011-04-28T15:42:10.533

17 The tangent bundle to an infinite-dimensional manifold 2011-05-25T04:41:07.797

17 Sheafification via hypercovers 2012-03-12T08:13:34.097

17 Understanding Adjointness of Sheaves in Algebraic Geometry 2013-02-22T05:03:04.970

17 Brouwer's theorem for the Cauchy reals 2015-08-28T03:04:51.387

17 Can $\mathcal O_X$ be recognized abstract-nonsensically? 2016-12-09T05:37:32.250

17 Is there an Infinite dimensional sheaf theory for analysis on manifolds? 2017-08-05T17:04:30.363

16 What is a section? 2009-12-06T22:16:16.920

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

16 Cohomology of Structure Sheaves: Algebraic, Constructible and more 2011-01-23T22:20:32.117

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

16 Is there a useful theory of D-modules on smooth (non-analytic) manifolds? 2017-03-03T08:39:40.753

15 Functorial characterization of open subschemes? 2009-10-20T03:49:51.093

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

15 Elementary short exact sequence of sheaves 2011-04-26T18:23:47.983

15 Why do rigid spaces have "not enough points"? 2013-05-19T08:22:44.607

15 Etale spaces using Kan extensions 2015-02-10T21:48:21.127

15 Characterize constant objects in the internal language of a topos? 2017-08-01T15:05:49.400

14 What representative examples of modules should I keep in mind? 2009-10-22T06:29:42.877

14 Which topological spaces have the property that their sheaves of continuous functions are determined by their global sections? 2009-11-20T06:24:21.840

14 Cohomology of a sheaf of functions locally constant along a foliation 2010-02-27T15:06:48.780

14 What are the merits of the different finiteness conditions on quasi-coherent sheaves? 2010-05-09T09:31:32.253

14 Locally constant sheaves for the étale topology, lack of intuition about "étale-localness" 2011-01-18T13:25:01.120

14 What's the easiest example of a morphism of topoi that is not from that of a site? 2011-10-31T01:24:10.940

14 Affine scheme on spec(A) of a ring A as the sheafification of a pre-sheave on spec(A)? 2011-11-10T02:58:37.963

14 Necessity of hypercovers for sheaf condition for simplicial sheaves 2012-02-03T12:43:41.110

14 The real numbers object in Sh(Top) 2014-10-31T23:07:59.207

14 Measuring a presheaf's failure to be a sheaf? 2017-08-20T11:07:34.087

13 References regarding a connection between recursion theory and sheaves 2010-05-19T22:08:28.510

13 Sheaf cohomology and inverse limits 2011-05-17T15:24:32.943

13 What information is lost in $X \to \mathrm{Sh}(X)$? 2014-05-30T20:37:18.200

13 Physical interpretations/meanings of the notion of a sheaf? 2016-11-13T21:48:24.523

13 Sheaves of complexes and complexes of sheaves 2017-03-25T21:35:40.810

13 Meaning of the determinant of cohomology 2017-04-19T00:10:20.257

12 Total Spaces of Quasicoherent Sheaves 2009-10-29T18:57:19.250

12 global fibrations of simplicial sheaves 2009-11-12T09:47:54.287

12 Understanding the etale space construction from a formal viewpoint 2010-08-18T19:16:08.010

12 Derived categories of coherent sheaves: suggested references? 2010-10-17T06:35:49.360

12 Cosheafification 2013-02-04T05:30:34.860

12 Hypercohomology of a complex via Cech cohomology 2013-04-08T06:50:42.610

12 Sheaves on Contractible Analytic Spaces 2013-05-22T13:50:46.437

12 Reference request: Book of topology from "Topos" point of view 2014-08-30T16:38:56.250

12 A bit of history of Verdier duality 2014-12-17T23:14:33.677

12 Which nice/deep elaborations on the (operators <-> sheaves) / (endomorphisms <-> objects) theme are there? 2015-07-08T17:30:27.460

12 Grothendieck - sheaves as meter sticks 2015-08-09T21:15:34.033

12 A sheaf is a presheaf that preserves small limits 2018-03-10T10:52:12.523

11 Does sheafification preserve sheaves for a different topology? 2009-12-07T17:15:12.000

11 Mitchell's embedding theorem 2010-07-16T14:04:45.943

11 Is there an easy way to describe the sheaf of smooth functions on a product manifold? 2010-09-01T20:53:36.567

11 Wikipedia's definition of 'locally free sheaf' 2010-11-04T16:08:14.303

11 Under what circumstances do morphisms on the stalks of a sheaf induce a sheaf morphism 2011-01-12T00:35:43.263

11 Coboundaries and Gluing in Cech Cohomology - Intuition? 2013-03-21T20:29:58.340

11 Reference request: sheaves on the site of d-manifolds 2015-09-30T16:11:54.450

11 Homotopy property of constructible sheaves on stratified spaces 2016-04-11T12:01:22.893

11 Sheaf associated to presheaf Aut 2017-02-08T22:45:30.690

10 Finiteness conditions on simplicial sheaves/presheaves 2009-10-16T00:41:18.953

10 When does the sheaf direct image functor f_* have a right adjoint? 2009-10-27T19:58:07.950

10 Why is an injective quasi-coherent sheaf's restriction to an open subset still an injective object? 2009-11-25T04:22:22.423

10 Wikipedia's definition of constant sheaf is wrong 2010-05-01T09:54:28.073

10 Do we have non-abelian sheaf cohomology? 2010-08-23T17:05:33.493

10 How do the direct and inverse image sheaf functors interact with homotopy? 2015-09-12T10:34:00.747

10 Examples of calculating perverse sheaves on algebraic varieties with easy stratification 2016-03-02T10:01:52.780

10 Polylogarithm sheaves 2016-06-23T17:25:56.437

10 Understanding the purely formal part of the sheaf theoretic (cohomological) framework for representation theory 2016-07-21T16:07:02.610

10 Donaldson and DT invariants 2017-07-12T16:06:49.787

10 What is the total space of a stack after all? 2017-07-30T06:29:49.247

9 Sheaves as full reflective subcategories 2010-02-28T12:26:41.553

9 Motivation for equivariant sheaves? 2010-04-07T17:54:31.443

9 Is the dual notion of a presheaf useful? 2010-07-15T21:45:20.463

9 Homotopical descent information contained in the Dwyer-Kan function complexes of a presheaf category? 2010-12-06T00:57:15.663

9 Sheaves of $\mathbb Z$-modules = sheaves of abelian groups 2011-06-13T22:07:02.800