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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A model structure on the category of pro-simplicial sets
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by Daniel C. Isaksen PDF
Trans. Amer. Math. Soc. 353 (2001), 2805-2841 Request permission

Abstract:

We study the category pro-$\mathcal {SS}$ of pro-simplicial sets, which arises in étale homotopy theory, shape theory, and pro-finite completion. We establish a model structure on pro-$\mathcal {SS}$ so that it is possible to do homotopy theory in this category. This model structure is closely related to the strict structure of Edwards and Hastings. In order to understand the notion of homotopy groups for pro-spaces we use local systems on pro-spaces. We also give several alternative descriptions of weak equivalences, including a cohomological characterization. We outline dual constructions for ind-spaces.
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Additional Information
  • Daniel C. Isaksen
  • Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
  • Address at time of publication: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
  • MR Author ID: 611825
  • Email: isaksen.1@nd.edu
  • Received by editor(s): October 12, 1999
  • Published electronically: January 29, 2001
  • Additional Notes: The author was supported in part by an NSF Graduate Fellowship
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 2805-2841
  • MSC (2000): Primary 18E35, 55Pxx, 55U35; Secondary 14F35, 55P60
  • DOI: https://doi.org/10.1090/S0002-9947-01-02722-2
  • MathSciNet review: 1828474