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Proceedings of the American Mathematical Society

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Fibers of partial totalizations of a pointed cosimplicial space


Authors: Akhil Mathew and Vesna Stojanoska
Journal: Proc. Amer. Math. Soc. 144 (2016), 445-458
MSC (2010): Primary 55U35, 55U40
DOI: https://doi.org/10.1090/proc/12699
Published electronically: June 5, 2015
MathSciNet review: 3415610
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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
Article copyright: © Copyright 2015 American Mathematical Society