The Action by Natural Transformations of a Group on a Diagram of Spaces
Abstract
For $\Cc$ 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.