Equivariant homotopy equivalence of homotopy colimits of $$G$$-functors

Abstract

AbstractGiven a group G and a G-category $${\textbf{C}}$$ C , we give a condition on a diagram of simplicial sets indexed by $${\textbf{C}}$$ C that allows us to define a natural action of G on its homotopy colimit, and some other simplicial sets defined in terms of the diagram. Well-known theorems on homeomorphisms and homotopy equivalences are generalized to equivariant versions.