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A model category structure on the category of simplicial categories
Author(s):
Julia
E.
Bergner
Journal:
Trans. Amer. Math. Soc.
359
(2007),
2043-2058.
MSC (2000):
Primary 18G55, 18D20
Posted:
December 19, 2006
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Abstract:
In this paper we put a cofibrantly generated model category structure on the category of small simplicial categories. The weak equivalences are a simplicial analogue of the notion of equivalence of categories.
References:
-
- 1.
- J.E. Bergner, Three models for the homotopy theory of homotopy theories, Ph.D. Thesis, University of Notre Dame, 2005.
- 2.
- William G. Dwyer, Philip S. Hirschhorn, Daniel M. Kan, and Jeffrey H. Smith, Homotopy limit functors on model categories and homotopical categories. Mathematical Surveys and Monographs, 113. American Mathematical Society, Providence, RI, 2004. MR 2102294 (2005k:18027)
- 3.
- W.G. Dwyer and D.M. Kan, Function complexes in homotopical algebra, Topology 19 (1980), 427-440. MR 0584566 (81m:55018)
- 4.
- W.G. Dwyer and D.M. Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980) 267-284. MR 0579087 (81h:55018)
- 5.
- W.G. Dwyer and J. Spalinski, Homotopy theories and model categories, in Handbook of Algebraic Topology, Elsevier, 1995. MR 1361887 (96h:55014)
- 6.
- P.G. Goerss and J.F. Jardine. Simplicial Homotopy Theory, Progress in Math, vol. 174, Birkhauser, 1999. MR 1711612 (2001d:55012)
- 7.
- Philip S. Hirschhorn, Model Categories and Their Localizations, Mathematical Surveys and Monographs 99, AMS, 2003. MR 1944041 (2003j:18018)
- 8.
- Mark Hovey, Model Categories, Mathematical Surveys and Monographs 63, AMS, 1999. MR 1650134 (99h:55031)
- 9.
- Jean-Pierre Serre, Groupes d'homotopie et classes de groupes abéliens, Ann. of Math, 58 (1953), 258-294. MR 0059548 (15:548c)
- 10.
- Bertrand Toën and Gabriele Vezzosi. Homotopical algebraic geometry I: topos theory, preprint available at math.AG/0207028.
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Additional Information:
Julia
E.
Bergner
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Address at time of publication:
Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, Kansas 66506
Email:
bergnerj@member.ams.org
DOI:
10.1090/S0002-9947-06-03987-0
PII:
S 0002-9947(06)03987-0
Received by editor(s):
January 28, 2005
Posted:
December 19, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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