Fibers of partial totalizations of a pointed cosimplicial space

Akhil Mathew, Vesna Stojanoska

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)445-458
Number of pages14
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Jan 2016
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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