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Transactions of the American Mathematical Society

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Replacing model categories with simplicial ones


Author: Daniel Dugger
Journal: Trans. Amer. Math. Soc. 353 (2001), 5003-5027
MSC (2000): Primary 55U35
DOI: https://doi.org/10.1090/S0002-9947-01-02661-7
Published electronically: April 11, 2001
MathSciNet review: 1852091
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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. 1, Encyclopedia of Mathematics and its Applications, vol. 50, Cambridge University Press, Cambridge, 1994. Basic category theory. MR 1291599
    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
    Francis Borceux, Handbook of categorical algebra. 3, Encyclopedia of Mathematics and its Applications, vol. 52, Cambridge University Press, Cambridge, 1994. Categories of sheaves. MR 1315049
  • [BK] A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
  • [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, https://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
  • [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-New York, 1967. MR 0223432
  • [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: https://doi.org/10.1090/S0002-9947-01-02661-7
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