The Action by Natural Transformations of a Group on a Diagram of Spaces

Details The Action by Natural Transformations of a Group on a Diagram of Spaces The Action by Natural Transformations of a Group on a Diagram of Spaces

2004-11-22

arxiv.org/abs/math/0411502v1

Mathematics

Algebraic Topology

8 pages

Scientific paper

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.

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