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 | References | Similar Articles | Additional Information

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

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