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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A model for the homotopy theory of homotopy theory


Author: Charles Rezk
Journal: Trans. Amer. Math. Soc. 353 (2001), 973-1007
MSC (2000): Primary 55U35; Secondary 18G30
Published electronically: June 20, 2000
MathSciNet review: 1804411
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Abstract:

We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, ``functors between two homotopy theories form a homotopy theory'', or more precisely that the category of such models has a well-behaved internal hom-object.


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Additional Information

Charles Rezk
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: rezk@math.nwu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02653-2
PII: S 0002-9947(00)02653-2
Keywords: Homotopy theory, simplicial spaces, localization, closed model categories
Received by editor(s): November 4, 1998
Published electronically: June 20, 2000
Article copyright: © Copyright 2000 American Mathematical Society