Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A model category structure on the category of simplicial categories

Author: Julia E. Bergner
Journal: Trans. Amer. Math. Soc. 359 (2007), 2043-2058
MSC (2000): Primary 18G55, 18D20
Published electronically: December 19, 2006
MathSciNet review: 2276611
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 18G55, 18D20

Retrieve articles in all journals with MSC (2000): 18G55, 18D20

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

Received by editor(s): January 28, 2005
Published electronically: December 19, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society