Fibers of partial totalizations of a pointed cosimplicial space

Mathew, Akhil; Stojanoska, Vesna

doi:10.1090/proc/12699

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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