## Fibers of partial totalizations of a pointed cosimplicial space

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- by Akhil Mathew and Vesna Stojanoska
- Proc. Amer. Math. Soc.
**144**(2016), 445-458 - DOI: https://doi.org/10.1090/proc/12699
- Published electronically: June 5, 2015
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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.## References

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## Bibliographic 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