Tag: model-categories

54 Do we still need model categories? 2011-10-17T23:57:59.800

49 What are surprising examples of Model Categories? 2010-03-16T04:36:08.120

43 What is modern algebraic topology(homotopy theory) about? 2016-01-14T07:45:29.343

39 Non-examples of model structures, that fail for subtle/surprising reasons? 2010-05-02T18:07:59.907

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

31 Why do we need model categories? 2017-11-27T14:50:46.313

31 Why is Voevodsky's motivic homotopy theory 'the right' approach? 2018-11-20T21:22:19.403

29 Homotopical algebra is not concrete 2017-02-03T16:09:37.660

26 The homotopy category is not complete nor cocomplete 2016-05-20T15:52:55.387

24 Fibrations and Cofibrations of spectra are "the same" 2014-07-28T08:32:17.297

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

21 Model structure on Simplicial Sets without using topological spaces 2010-11-14T23:54:34.643

21 How canonical is cofibrant replacement? 2011-02-06T06:33:37.827

20 Limitations on model-categorical presentations 2012-04-29T17:18:06.293

20 Joyal's letter to Grothendieck 2014-12-19T11:17:38.697

19 How many model categories have the same weak equivalences? 2010-07-01T04:34:42.283

18 Derived categories and homotopy categories 2009-10-12T19:15:48.873

18 Is there a combinatorial way to factor a map of simplicial sets as a weak equivalence followed by a fibration? 2010-04-26T20:18:30.550

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

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

17 Are non-empty finite sets a Grothendieck test category? 2010-01-07T16:47:46.963

17 Homotopy Limits over Fibered Categories 2010-03-07T22:35:27.363

17 Homotopy colimits/limits using model categories 2010-03-29T20:56:28.020

17 A model category of abelian categories? 2015-05-11T22:10:35.107

16 Model structure of commutative dg-algebras inside all dg-algebras 2009-11-11T10:45:03.257

16 Homotopy pullbacks and homotopy pushouts 2009-12-12T16:16:41.830

16 Is there an additive model of the stable homotopy category? 2010-03-03T11:20:10.003

16 Is there an ∞-categorical interpretation of the Quillen S⁻¹S construction? 2015-11-29T12:30:29.327

15 What are the fibrant objects in the injective model structure? 2009-12-21T17:08:09.070

15 Model category structure on Set without axiom of choice 2009-12-31T07:07:40.717

15 What determines a model structure? 2010-06-26T19:14:16.023

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

15 From relative categories to marked simplicial sets 2016-04-08T15:29:59.780

15 Why is every object cofibrant in an excellent model category? 2016-06-24T15:39:33.500

15 What are the advantages of various "models" for the motivic stable homotopy category 2017-04-25T22:27:00.760

15 Do combinatorial model categories and Quillen adjunctions model presentable $\infty$-categories? 2018-05-03T22:20:04.380

15 Homotopy theories of operads 2018-07-17T04:45:36.827

14 Categories which are not compactly generated 2009-11-11T01:11:40.930

14 Pointed Hurewicz model structure 2010-11-30T04:29:52.527

14 Model category structure on categories enriched over quasi-coherent sheaves 2011-03-27T19:45:19.973

14 When is the category of pro-objects a homotopy category? 2012-03-03T02:17:48.957

14 When do colimits agree with homotopy colimits? 2016-04-07T01:26:57.983

14 Geometric Meaning of Different K-theories 2016-09-06T01:39:16.840

13 Are generalized cohomology theories a homotopy category of some category of invariants? 2009-10-21T10:15:48.593

13 A Model Category of Segal Spaces? 2010-06-27T19:59:48.790

13 Model for the (infinity,1)-category of (homotopy-)limit preserving functors 2012-12-26T16:46:30.063

13 The category theory of $(\infty, 1)$-categories 2013-04-11T08:55:22.837

13 Quasicategories for non-simplicial model categories 2015-08-11T12:20:18.630

13 Fibrant-cofibrant models of Eilenberg-MacLane spectra 2015-09-11T01:01:38.423

13 What is a model category from an $\infty$ point of view? 2018-04-28T21:02:29.987

13 Weak complicial sets: Are the morphisms too strict? 2018-05-03T00:45:37.770

12 Model category structures on categories of complexes in abelian categories 2009-10-06T18:17:25.733

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

12 Model Structure/Homotopy Pushouts in topological monoids? 2010-01-07T19:01:00.177

12 How to localize a model category with respect to a class of maps created by a left Quillen functor 2010-03-25T14:50:51.470

12 Is the model category of Complete Segal Spaces right proper? 2010-10-03T15:32:24.083

12 Do homotopy groups "always" commute with filtered colimits? 2011-02-21T11:58:26.053

12 Is the simplicial completion of a localizer always a bousfield localization of the injective model structure? 2011-06-16T15:21:59.480

12 The weak equivalences in the covariant model structure 2011-08-28T01:09:18.290

12 Computations in $\infty$-categories 2011-12-27T12:34:12.810

12 Examples of differential cohomology in cohesive $\infty$ topos 2015-11-01T10:08:56.900

12 Simple question: different definitions of Bousfield localization 2015-11-25T11:03:59.377

12 Non-Cartesian Monoidal Model Structure on a Slice Category 2016-01-26T21:12:35.930

12 Is there an analog of Kan's $Ex_\infty$ functor for quasicategories? 2016-11-20T00:18:57.563

11 What is the "universal problem" that motivates the definition of homotopy limits/colimits (and more generally "derived" functors)? 2010-09-08T11:58:00.920

11 Model category structures on dga's in a ringed topos 2013-01-25T18:07:10.770

11 Model structure on the category of small $A_\infty$ categories, hocolims. 2013-04-10T00:20:11.237

11 The state of the art in the rectification of homotopy-coherent structures 2013-09-03T21:12:30.973

11 Model structure for cooperads and for coalgebras 2013-11-11T23:08:47.197

11 The definition of Reedy category 2014-07-24T16:24:24.370

11 Property-like structure in a model category 2017-11-06T23:14:46.390

10 Example of a CW complex not homeomorphic to the realization of a simplicial set? 2010-08-05T19:14:16.733

10 Non standard (?) model category structure on (co)chain complexes. 2010-10-19T08:25:23.747

10 "Strøm-type" model structure on chain complexes? 2011-01-19T12:34:59.767

10 Hovey's unit axiom in monoidal model categories 2012-01-10T12:54:04.723

10 How many model category structures are there on Top? 2012-05-18T20:26:29.323

10 Fubini theorem for hocolim. 2012-10-25T13:50:29.540

10 Is there a notion of a “model category which admits left Bousfield localization?” 2012-10-29T19:23:48.257

10 Which statements and arguments of Hovey's "Model categories" fail without functorial factorizations of morphisms? 2013-11-30T13:54:51.647

10 Constructing a "geometric" model structure on Cat by localizing the "categorical" model structure 2014-07-20T08:01:52.890

10 Small objects vs Compact objects 2014-12-03T10:52:47.913

10 Categorical or simplicial introduction to modern homotopy theory 2015-11-21T08:35:43.743

10 When is a functor a right derived functor? 2016-07-18T15:06:02.780

10 The cofibration/fibration $\leftrightarrow$ epi/mono confusion 2017-11-30T14:27:59.513

10 When does the forgetful functor from algebras over a monad commute with homotopy geometric realizations? 2018-04-09T12:12:26.863

10 Is every symmetric monoidal combinatorial model category symmetric monoidally Quillen equivalent to a simplicial such? 2018-05-09T01:03:46.977

10 Is there an "injective version" of the Bergner model structure? 2018-06-26T19:53:09.637

9 Is model structure on CatSet unique? 2010-03-19T13:38:23.387

9 Infinity groupoid objects 2010-03-20T14:10:33.113

9 When do the Reedy and injective model category structures agree? 2010-03-30T02:25:09.203

9 Schemes as a model category 2010-06-29T15:36:58.753

9 Is the injective model structure on symmetric spectra Bousfield localizable? 2010-10-19T13:23:38.213

9 Model for the (infinity,1)-category of functors preserving certain homotopy limits 2012-12-27T05:11:40.493

9 When is the projective model structure cartesian? When is the internal hom invariant? 2013-03-06T10:09:53.357

9 Seeking errata for Berger-Moerdijk Axiomatic Homotopy Theory for Operads 2013-05-03T16:30:08.753

9 Where should I search for resolutions? 2013-07-13T11:43:20.843

9 Reference for a generalization of Γ-spaces to monoidal model categories 2014-01-16T16:01:12.907

9 Homotopy theory of suplattices 2014-03-23T18:28:12.797

9 When does a sheaf of categories represent a homotopy sheaf? 2014-07-03T16:32:11.883