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

Change of universe functors in equivariant stable homotopy theory

One striking difference between nonequivariant and equivariant stable homotopy is that, in the equivariant context, one must specify those representations with respect to which spectra are to be stable. One may specify stability with respect only to trivial representations (thereby obtaining what is often called the naive equivariant stable category), with respect to all representations (thereb...

Homotopy (limits And) Colimits

These notes were written to accompany two talks given in the Algebraic Topology and Category Theory Proseminar at the University of Chicago in Winter 2009. When a category has some notion of limits and colimits associated to it, its ordinary limits and colimits are not necessarily homotopically meaningful. We describe a notion of a “homotopy colimit” for two sorts of categories with a homotopy ...

Homotopy colimits in model categories

A Primer on Homotopy Colimits

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences