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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fibers of partial totalizations of a pointed cosimplicial space
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by Akhil Mathew and Vesna Stojanoska PDF
Proc. Amer. Math. Soc. 144 (2016), 445-458 Request permission

Abstract:

Let $X^\bullet$ be a cosimplicial object in a pointed $\infty$-category. We show that the fiber of $\mathrm {Tot}_m(X^\bullet ) \to \mathrm {Tot}_n(X^\bullet )$ depends only on the pointed cosimplicial object $\Omega ^k X^\bullet$ and is in particular a $k$-fold loop object, where $k = 2n - m+2$. The approach is explicit obstruction theory with quasicategories. We also discuss generalizations to other types of homotopy limits and colimits.
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Additional Information
  • Akhil Mathew
  • Affiliation: Department of Mathematics, University of California, Berkeley, California, 94720
  • MR Author ID: 891016
  • Email: amathew@math.berkeley.edu
  • Vesna Stojanoska
  • Affiliation: Max Planck Institute for Mathematics, Bonn, Germany, 53111
  • MR Author ID: 857759
  • Email: vstojanoska@mpim-bonn.mpg.de
  • Received by editor(s): August 12, 2014
  • Received by editor(s) in revised form: December 10, 2014, and December 18, 2014
  • Published electronically: June 5, 2015
  • Additional Notes: The first author was partially supported by the NSF Graduate Research Fellowship under grant DGE-110640
    The second author was partially supported by NSF grant DMS-1307390
  • Communicated by: Michael A. Mandell
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 445-458
  • MSC (2010): Primary 55U35, 55U40
  • DOI: https://doi.org/10.1090/proc/12699
  • MathSciNet review: 3415610