Fibers of partial totalizations of a pointed cosimplicial space

الأصل · EN

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.