Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

Compositio Mathematica

Volumn 141, Issue 1, 2005, Pages 253-261

  Kock, Joachim ^a   Toën, Bertrand ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Deligne conjecture; Hochschild cohomology; Model categories; Simplicial categories

Indexed keywords

EID: 33846834972     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0010437X04001009     Document Type: Article

References (29)

1. n-spaces, Preprint (2002), math.CT/0207281.
2. C. Berger and B. Fresse, Combinatorial operad actions on cochains, Math. Proc. Cambridge Philos. Soc. 137 (2004), 135-174.
3. C. Bǎlteanu, Z. Fiedorowicz, R. Schwänzl and R. Vogt, Iterated monoidal categories, Adv. Math. 176 (2003), 277-349.
4. W. G. Dwyer and D. M. Kan, Function complexes in homotopical algebra, Topology 19 (1980), 427-440.
5. W. G. Dwyer and D. M. Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980), 267-284.
6. E. Getzler and J. D. S. Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, Preprint (1994), hep-th/9403055.
7. M. Gerstenhaber and A. A. Voronov, Homotopy G-algebras and moduli space operad, Int. Math. Res. Not. (1995), 141-153 (electronic).
8. P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergeb. Math. Grenzgeb., vol. 35 (Springer, New York, 1967).
9. P. S. Hirschhorn, Model categories and their localizations, Mathematical Surveys and Monographs, vol. 99 (American Mathematical Society, Providence, RI, 2003). (A preliminary version was widely circulated under the title Localization of model categories. This is the version to which we actually refer.)
10. P. Hu, I. Kriz and A. A. Voronov, On Kontsevich's Hochschild cohomology conjecture, Preprint (2003), math.AT/0309369.
11. M. Hovey, Model categories, Mathematical Surveys and Monographs, vol. 63 (American Mathematical Society, Providence, RI, 1999).
12. A. Hirschowitz and C. Simpson, Descente pour les n-champs, Preprint (1998), math.AG/9807049.
13. L. Illusie, Complexe cotangent et déformations. I, Lecture Notes in Mathematics, vol. 239 (Springer, Berlin, 1971).
14. A. Joyal and R. Street, Braided tensor categories, Adv. Math. 102 (1993), 20-78.
15. J. Kock, A notion of weak identity arrows in higher categories, Preprint (2004). Available from the author's web page.
16. M. Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999), 35-72.
17. M. Kontsevich and Y. Soibelman, Deformations of algebras over operads and the Deligne conjecture, in Conférence Moshé Flato (Dijon 1999) I, Mathematical Physics Studies, vol. 21 (Kluwer, Dordrecht, 2000), 255-307.
18. T. Leinster, Homotopy algebras for operads, Preprint (2000), math.CT/0002180.
19. J. E. McClure and J. H. Smith, A solution of Deligne's Hochschild cohomology conjecture, in Recent progress in homotopy theory (Baltimore, MD, 2000), Contemporary Mathematics, vol. 293 (American Mathematical Society, Providence, RI, 2002), 153-193.
20. D. Quillen, Homotopical algebra, Lecture Notes in Mathematics, vol. 43 (Springer, Berlin, 1967).
21. G. Segal, Categories and cohomology theories, Topology 13 (1974), 293-312.
22. M. Spitzweck, Operads, algebras and modules in model categories and motives, PhD thesis, University of Bonn (2001).
23. S. Schwede and B. Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3) 80 (2000), 491-511.
24. n, Preprint (1998), math.QA/9803025.
25. D. E. Tamarkin, Deformation complex of a d-algebra is a (d + 1)-algebra, Preprint (2000), math.Q A/0010072.
26. Z. Tamsamani. Sur des notions de n-catégorie et n-groupoïde non strictes via des ensembles multi-simpliciaux, K-Theory 16 (1999), 51-99.
27. B. Toën, Homotopical and higher categorical structures in algebraic geometry, Preprint (2003), math.AG/0312262.
28. B. Toën and G. Vezzosi, Segal topoi and stacks over Segal categories, Preprint (2002), math.AG/0212330.
29. A. A. Voronov, Homotopy Gerstenhaber algebras, in Conférence Moshé Flato (Dijon 1999), II, Mathematical Physics Studies, vol. 22 (Kluwer, Dordrecht, 2000), 307-331.