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.
ASJC Scopus subject areas
- Applied Mathematics