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)



Replacing model categories with simplicial ones

Author: Daniel Dugger
Journal: Trans. Amer. Math. Soc. 353 (2001), 5003-5027
MSC (2000): Primary 55U35
Published electronically: April 11, 2001
MathSciNet review: 1852091
Full-text PDF

Abstract | References | Similar Articles | Additional Information


In this paper we show that model categories of a very broad class can be replaced up to Quillen equivalence by simplicial model categories.

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

  • [B] F. Borceux, Handbook of categorical algebra II, Categories and structures, Cambridge University Press, 1994. MR 96g:18001b
  • [BK] A.K. Bousfield and D.M. Kan, Homotopy limits, completions, and localizations, Springer Lecture Notes in Math. 304, Springer-Verlag, New York, 1972. MR 51:1825
  • [CS] W. Chachólski and J. Scherer, Homotopy meaningful constructions: Homotopy colimits, 1998, preprint.
  • [DHK] W. G. Dwyer, P. S. Hirschhorn, D. M. Kan, Model categories and more general abstract nonsense, in preparation.
  • [DKS] W. G. Dwyer, D. M. Kan, C. R. Stover, An $E_2$model category structure for pointed simplicial spaces, J. Pure Appl. Alg. 90 (1993), pp. 137-152. MR 95c:55027
  • [H] P. S. Hirschhorn, Localization of Model Categories, 1998 preprint. (Available at$\sim$psh).
  • [Ho] M. Hovey, Model Categories, Mathematical Surveys and Monographs vol. 63, Amer. Math. Soc., 1999. MR 99h:55031
  • [McL] S. Mac Lane, Categories for the Working Mathematician, Grad. Texts in Math., Vol. 5, Springer-Verlag, New York, 1971. CMP 2000:01
  • [Q] D. Quillen, Homotopical Algebra, Springer Lecture Notes in Math. 43, Springer-Verlag, Berlin, 1967. MR 36:6480
  • [R] C. Rezk, Fibrations and homotopy colimits of simplicial presheaves, 1998 Preprint.
  • [RSS] C. Rezk, S. Schwede, and B. Shipley, Simplicial Model Categories, in preparation.
  • [S] J. Smith, Combinatorial model categories, in preparation.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 55U35

Retrieve articles in all journals with MSC (2000): 55U35

Additional Information

Daniel Dugger
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Received by editor(s): December 8, 1998
Received by editor(s) in revised form: December 1, 1999
Published electronically: April 11, 2001
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society