2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221282In this note, we discuss the derived functors of infinite products and homotopy limits. $QC(X)$, the category of quasi-coherent sheaves on a Deligne-Mumford stack $X$, usually has the property that the derived functors of product vanish after a finite stage. We use this fact to study the convergence of certain homotopy limits and apply it compare the derived category of $QC(X)$ with certain other closely related triangulated categories.13 pagesCategory TheoryAlgebraic Geometry18E30, 14A20text