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Transactions of the American Mathematical Society
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
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Abstract | References | Similar Articles | Additional Information

Abstract:

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] Francis Borceux, Handbook of categorical algebra. 2, Encyclopedia of Mathematics and its Applications, vol. 51, Cambridge University Press, Cambridge, 1994. Categories and structures. MR 1313497 (96g:18001b)
  • [BK] A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin, 1972. MR 0365573 (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, and C. R. Stover, An 𝐸² model category structure for pointed simplicial spaces, J. Pure Appl. Algebra 90 (1993), no. 2, 137–152. MR 1250765 (95c:55027), http://dx.doi.org/10.1016/0022-4049(93)90126-E
  • [H] P. S. Hirschhorn, Localization of Model Categories, 1998 preprint. (Available at http://www-math.mit.edu/$\sim$psh).
  • [Ho] Mark Hovey, Model categories, Mathematical Surveys and Monographs, vol. 63, American Mathematical Society, Providence, RI, 1999. MR 1650134 (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] Daniel G. Quillen, Homotopical algebra, Lecture Notes in Mathematics, No. 43, Springer-Verlag, Berlin, 1967. MR 0223432 (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.

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Additional Information

Daniel Dugger
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: ddugger@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02661-7
PII: S 0002-9947(01)02661-7
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