2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73336For $\Cc$ a $G$-category, we give a condition on a diagram of simplicial sets indexed on $\Cc$ that allows us to define a natural $G$-action on its homotopy colimit, and in some other simplicial sets and categories defined in terms of the diagram. Well-known theorems on homeomorphisms and homotopy equivalences are generalized to an equivariant version.8 pagesAlgebraic Topology55P91text