Fibers of partial totalizations of a pointed cosimplicial space

Akhil Mathew; Vesna Stojanoska

doi:10.1090/proc/12699

Fibers of partial totalizations of a pointed cosimplicial space

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Abstract

Let X• be a cosimplicial object in a pointed ∞-category. We show that the fiber of Totm(X•) → Tot_n(X•) depends only on the pointed cosimplicial object Ω^k X• 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.

Original language	English (US)
Pages (from-to)	445-458
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	1
DOIs	https://doi.org/10.1090/proc/12699
State	Published - Jan 2016
Externally published	Yes

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General Mathematics
Applied Mathematics

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10.1090/proc/12699

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abstract = "Let X• be a cosimplicial object in a pointed ∞-category. We show that the fiber of Totm(X•) → Totn(X•) depends only on the pointed cosimplicial object Ωk X• 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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Fibers of partial totalizations of a pointed cosimplicial space

Abstract

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