  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.

Algebraic Topology;Category Theory