Nous construisons une structure de catégorie de modèles de Quillen à engendrement cofibrant sur la catégorie des petites catégories différentielles graduées.
We construct a cofibrantly generated Quillen model structure on the category of small differential graded categories.
Accepté le :
Publié le :
Goncalo Tabuada 1
@article{CRMATH_2005__340_1_15_0, author = {Goncalo Tabuada}, title = {Une structure de cat\'egorie de mod\`eles de {Quillen} sur la cat\'egorie des dg-cat\'egories}, journal = {Comptes Rendus. Math\'ematique}, pages = {15--19}, publisher = {Elsevier}, volume = {340}, number = {1}, year = {2005}, doi = {10.1016/j.crma.2004.11.007}, language = {fr}, }
Goncalo Tabuada. Une structure de catégorie de modèles de Quillen sur la catégorie des dg-catégories. Comptes Rendus. Mathématique, Volume 340 (2005) no. 1, pp. 15-19. doi : 10.1016/j.crma.2004.11.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.007/
[1] A model category structure on the category of simplicial categories | arXiv
[2] DG quotients of DG categories, J. Algebra, Volume 272 (2004), pp. 643-691
[3] Simplicial localizations of categories, J. Pure Appl. Algebra, Volume 17 (1980), pp. 267-284
[4] Model Categories, Math. Surveys Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999
[5] Strong stacks and classifying spaces, Category Theory, Lecture Notes in Math., vol. 1488, Springer, Berlin, 1991
[6] Deriving DG categories, Ann. Sci. École Norm. Sup., Volume 27 (1994), pp. 63-102
[7] C. Rezk, A note on a certain model category structure on the category of categories, available at http://www.math.uiuc.edu/~rezk
[8] Une structure de catégorie de modèles de Quillen sur la catégorie des dg-catégories | arXiv
[9] The homotopy theory of dg-categories and derived Morita theory | arXiv
- Stacks, Encyclopedia of Mathematical Physics (2025), p. 522 | DOI:10.1016/b978-0-323-95703-8.00026-4
- Non-commutative nature of ℓ-adic vanishing cycles, Journal für die reine und angewandte Mathematik (Crelles Journal) (2025) | DOI:10.1515/crelle-2024-0099
- Formality and strongly unique enhancements, Journal of Algebra, Volume 667 (2025), p. 690 | DOI:10.1016/j.jalgebra.2025.01.002
- AUSLANDER–IYAMA CORRESPONDENCE FOR EXACT DG CATEGORIES, Nagoya Mathematical Journal (2025), p. 1 | DOI:10.1017/nmj.2025.6
- The dg Leavitt algebra, singular Yoneda category and singularity category, Advances in Mathematics, Volume 440 (2024), p. 109541 | DOI:10.1016/j.aim.2024.109541
- Formal contact categories, Algebraic Geometric Topology, Volume 24 (2024) no. 5, p. 2389 | DOI:10.2140/agt.2024.24.2389
- Categorical wall-crossing formula for Donaldson–Thomas theory on the resolved conifold, Geometry Topology, Volume 28 (2024) no. 3, p. 1341 | DOI:10.2140/gt.2024.28.1341
- An algebraic model for the free loop space, Higher Structures in Topology, Geometry, and Physics, Volume 802 (2024), p. 23 | DOI:10.1090/conm/802/16071
- The Simplicial Coalgebra of Chains Under Three Different Notions of Weak Equivalence, International Mathematics Research Notices, Volume 2024 (2024) no. 16, p. 11766 | DOI:10.1093/imrn/rnae031
- A functorial approach to rank functions on triangulated categories, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 0 (2024) no. 0 | DOI:10.1515/crelle-2024-0009
- Relative cluster categories and Higgs categories, Advances in Mathematics, Volume 424 (2023), p. 109040 | DOI:10.1016/j.aim.2023.109040
- Non-commutative derived moduli prestacks, Advances in Mathematics, Volume 433 (2023), p. 109300 | DOI:10.1016/j.aim.2023.109300
- The twisted tensor product of dg categories and a contractible 2-operad, Advances in Mathematics, Volume 434 (2023), p. 109310 | DOI:10.1016/j.aim.2023.109310
- Singular Equivalences Induced by Bimodules and Quadratic Monomial Algebras, Algebras and Representation Theory, Volume 26 (2023) no. 2, p. 609 | DOI:10.1007/s10468-021-10104-3
- Legendrian weaves : N–graph calculus, flag moduli and applications, Geometry Topology, Volume 26 (2023) no. 8, p. 3589 | DOI:10.2140/gt.2022.26.3589
- Categorical Donaldson–Thomas Theory for Local Surfaces: ℤ/2-Periodic Version, International Mathematics Research Notices, Volume 2023 (2023) no. 13, p. 11172 | DOI:10.1093/imrn/rnac142
- On the Composition of Two Spherical Twists, International Mathematics Research Notices, Volume 2023 (2023) no. 20, p. 17270 | DOI:10.1093/imrn/rnac249
- A CATEGORIFICATION OF ACYCLIC PRINCIPAL COEFFICIENT CLUSTER ALGEBRAS, Nagoya Mathematical Journal, Volume 252 (2023), p. 769 | DOI:10.1017/nmj.2023.6
- Ginzburg algebras of triangulated surfaces and perverse schobers, Forum of Mathematics, Sigma, Volume 10 (2022) | DOI:10.1017/fms.2022.1
- Uniqueness of enhancements for derived and geometric categories, Forum of Mathematics, Sigma, Volume 10 (2022) | DOI:10.1017/fms.2022.82
- Derived Traces of Soergel Categories, International Mathematics Research Notices, Volume 2022 (2022) no. 15, p. 11304 | DOI:10.1093/imrn/rnab019
- On the tensor product of well generated dg categories, Journal of Pure and Applied Algebra, Volume 226 (2022) no. 3, p. 106843 | DOI:10.1016/j.jpaa.2021.106843
- ENHANCED FINITE TRIANGULATED CATEGORIES, Journal of the Institute of Mathematics of Jussieu, Volume 21 (2022) no. 3, p. 741 | DOI:10.1017/s1474748020000250
- The derived deformation theory of a point, Mathematische Zeitschrift, Volume 300 (2022) no. 3, p. 3023 | DOI:10.1007/s00209-021-02892-7
- Motivic and
-adic realizations of the category of singularities of the zero locus of a global section of a vector bundle, Selecta Mathematica, Volume 28 (2022) no. 2 | DOI:10.1007/s00029-021-00734-2 - Singularity categories via the derived quotient, Advances in Mathematics, Volume 381 (2021), p. 107631 | DOI:10.1016/j.aim.2021.107631
- t-structures and twisted complexes on derived injectives, Advances in Mathematics, Volume 387 (2021), p. 107826 | DOI:10.1016/j.aim.2021.107826
- Derived Categories, Algebra and Applications 1 (2021), p. 321 | DOI:10.1002/9781119818175.ch9
- Hochschild (Co)homology and Derived Categories, Bulletin of the Iranian Mathematical Society, Volume 47 (2021) no. S1, p. 57 | DOI:10.1007/s41980-021-00556-0
- Homotopy limits in the category of dg-categories in terms of
-comodules, European Journal of Mathematics, Volume 7 (2021) no. 2, p. 671 | DOI:10.1007/s40879-020-00439-4 - Bar Category of Modules and Homotopy Adjunction for Tensor Functors, International Mathematics Research Notices, Volume 2021 (2021) no. 2, p. 1353 | DOI:10.1093/imrn/rnaa066
- Finite generation of cohomology for Drinfeld doubles of finite group schemes, Selecta Mathematica, Volume 27 (2021) no. 2 | DOI:10.1007/s00029-021-00637-2
- Liftable derived equivalences and objective categories, Bulletin of the London Mathematical Society, Volume 52 (2020) no. 5, p. 816 | DOI:10.1112/blms.12364
- Augmentations are sheaves, Geometry Topology, Volume 24 (2020) no. 5, p. 2149 | DOI:10.2140/gt.2020.24.2149
- Categorical smooth compactifications and generalized Hodge-to-de Rham degeneration, Inventiones mathematicae, Volume 222 (2020) no. 2, p. 667 | DOI:10.1007/s00222-020-00980-9
- Gluing semi-orthogonal decompositions, Journal of Algebra, Volume 559 (2020), p. 1 | DOI:10.1016/j.jalgebra.2020.03.022
- Topological Fukaya category and mirror symmetry for punctured surfaces, Compositio Mathematica, Volume 155 (2019) no. 3, p. 599 | DOI:10.1112/s0010437x19007073
- Formality conjecture for K3 surfaces, Compositio Mathematica, Volume 155 (2019) no. 5, p. 902 | DOI:10.1112/s0010437x19007206
- 2-Segal Spaces from Higher Categories, Higher Segal Spaces, Volume 2244 (2019), p. 107 | DOI:10.1007/978-3-030-27124-4_7
- A 2-Calabi–Yau realization of finite-type cluster algebras with universal coefficients, Mathematische Zeitschrift, Volume 291 (2019) no. 3-4, p. 1495 | DOI:10.1007/s00209-019-02261-5
- On the homotopy finiteness of DG categories, Russian Mathematical Surveys, Volume 74 (2019) no. 3, p. 431 | DOI:10.1070/rm9887
- О гомотопической конечности DG-категорий, Успехи математических наук, Volume 74 (2019) no. 3(447), p. 63 | DOI:10.4213/rm9887
- Shifted Poisson structures and moduli spaces of complexes, Advances in Mathematics, Volume 338 (2018), p. 991 | DOI:10.1016/j.aim.2018.09.018
- Generalized Tilting Theory, Applied Categorical Structures, Volume 26 (2018) no. 2, p. 309 | DOI:10.1007/s10485-017-9495-x
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c A ∞ -Categories and Functor Categories, Applied Categorical Structures, Volume 26 (2018) no. 5, p. 943 | DOI:10.1007/s10485-018-9526-2 - How to glue derived categories, Bulletin of Mathematical Sciences, Volume 8 (2018) no. 3, p. 477 | DOI:10.1007/s13373-018-0119-z
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- -homotopy invariants of topological Fukaya categories of surfaces, Compositio Mathematica, Volume 153 (2017) no. 8, p. 1673 | DOI:10.1112/s0010437x17007205
- All Autoequivalences are Spherical Twists, International Mathematics Research Notices (2017), p. rnw326 | DOI:10.1093/imrn/rnw326
- Recollements and stratifying ideals, Journal of Algebra, Volume 484 (2017), p. 47 | DOI:10.1016/j.jalgebra.2017.04.003
- A tour about existence and uniqueness of dg enhancements and lifts, Journal of Geometry and Physics, Volume 122 (2017), p. 28 | DOI:10.1016/j.geomphys.2016.11.030
- Systèmes de points dans les dg-catégories saturées, Annales de la Faculté des sciences de Toulouse : Mathématiques, Volume 25 (2016) no. 2-3, p. 583 | DOI:10.5802/afst.1506
- The uniqueness problem of dg‐lifts and Fourier‐Mukai kernels, Journal of the London Mathematical Society, Volume 94 (2016) no. 2, p. 617 | DOI:10.1112/jlms/jdw052
- K-theory and the bridge from motives to noncommutative motives, Advances in Mathematics, Volume 269 (2015), p. 399 | DOI:10.1016/j.aim.2014.10.011
- Internal Homs via extensions of dg functors, Advances in Mathematics, Volume 277 (2015), p. 100 | DOI:10.1016/j.aim.2015.03.004
- Enriched ∞-categories via non-symmetric ∞-operads, Advances in Mathematics, Volume 279 (2015), p. 575 | DOI:10.1016/j.aim.2015.02.007
- Dwyer-Kan homotopy theory of enriched categories, Journal of Topology, Volume 8 (2015) no. 2, p. 377 | DOI:10.1112/jtopol/jtu029
- Artin–Tate motivic sheaves with finite coefficients over an algebraic variety, Proceedings of the London Mathematical Society, Volume 111 (2015) no. 6, p. 1402 | DOI:10.1112/plms/pdv057
- Mirror Symmetry in Dimension 1 and Fourier–Mukai Transforms, Homological Mirror Symmetry and Tropical Geometry, Volume 15 (2014), p. 407 | DOI:10.1007/978-3-319-06514-4_10
- Ribbon graphs and mirror symmetry, Selecta Mathematica, Volume 20 (2014) no. 4, p. 979 | DOI:10.1007/s00029-014-0149-7
- Derived representation schemes and cyclic homology, Advances in Mathematics, Volume 245 (2013), p. 625 | DOI:10.1016/j.aim.2013.06.020
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- Derived Azumaya algebras and generators for twisted derived categories, Inventiones mathematicae, Volume 189 (2012) no. 3, p. 581 | DOI:10.1007/s00222-011-0372-1
- Symmetric monoidal structure on non-commutative motives, Journal of K-Theory, Volume 9 (2012) no. 2, p. 201 | DOI:10.1017/is011011005jkt169
- Compact generators in categories of matrix factorizations, Duke Mathematical Journal, Volume 159 (2011) no. 2 | DOI:10.1215/00127094-1415869
- Deformed Calabi–Yau completions, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2011 (2011) no. 654 | DOI:10.1515/crelle.2011.031
- Generalized spectral categories, topological Hochschild homology and trace maps, Algebraic Geometric Topology, Volume 10 (2010) no. 1, p. 137 | DOI:10.2140/agt.2010.10.137
- Noncommutative Geometry in the Framework of Differential Graded Categories, Arithmetic and Geometry Around Quantization (2010), p. 253 | DOI:10.1007/978-0-8176-4831-2_9
- On Drinfeld's DG quotient, Journal of Algebra, Volume 323 (2010) no. 5, p. 1226 | DOI:10.1016/j.jalgebra.2009.12.020
- Rational homotopy theory and differential graded category, Journal of Pure and Applied Algebra, Volume 214 (2010) no. 4, p. 422 | DOI:10.1016/j.jpaa.2009.06.015
- Differential graded versus simplicial categories, Topology and its Applications, Volume 157 (2010) no. 3, p. 563 | DOI:10.1016/j.topol.2009.10.015
- A Survey of (∞, 1)-Categories, Towards Higher Categories, Volume 152 (2010), p. 69 | DOI:10.1007/978-1-4419-1524-5_2
- Parametrizing recollement data for triangulated categories, Journal of Algebra, Volume 322 (2009) no. 4, p. 1220 | DOI:10.1016/j.jalgebra.2009.04.035
- Homotopy theory of well-generated algebraic triangulated categories, Journal of K-Theory, Volume 3 (2009) no. 1, p. 53 | DOI:10.1017/is007011019jkt021
- Higher K-theory via universal invariants, Duke Mathematical Journal, Volume 145 (2008) no. 1 | DOI:10.1215/00127094-2008-049
- Bounded derived categories and repetitive algebras, Journal of Algebra, Volume 319 (2008) no. 4, p. 1611 | DOI:10.1016/j.jalgebra.2007.10.001
- Dénombrabilité des classes d’équivalences dérivées de variétés algébriques, Journal of Algebraic Geometry, Volume 18 (2008) no. 2, p. 257 | DOI:10.1090/s1056-3911-08-00487-6
- Topological equivalences for differential graded algebras, Advances in Mathematics, Volume 212 (2007) no. 1, p. 37 | DOI:10.1016/j.aim.2006.09.013
- The homotopy theory of dg-categories and derived Morita theory, Inventiones mathematicae, Volume 167 (2007) no. 3, p. 615 | DOI:10.1007/s00222-006-0025-y
- Derived Hall algebras, Duke Mathematical Journal, Volume 135 (2006) no. 3 | DOI:10.1215/s0012-7094-06-13536-6
- Addendum a << Invariants additifs de dg-categories >>, International Mathematics Research Notices (2006) | DOI:10.1155/imrn/2006/75853
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