Author: Mark Hovey
Title: Homotopy theory of comodules over a Hopf algebroid
Given a good homology theory E and a topological space X, the E-homology
of X is not just an E_{*}-module but also a comodule over the Hopf
algebroid (E_{*}, E_{*}E). We establish a framework for studying the
homological algebra of comodules over a well-behaved Hopf algebroid (A,
Gamma ). That is, we construct the derived category Stable(Gamma) of
(A, Gamma) as the homotopy category of a Quillen model structure on the
category of unbounded chain complexes of Gamma-comodules. This derived
category is obtained by inverting the homotopy isomorphisms,
NOT the homology isomorphisms. We establish the basic
properties of Stable(Gamma), showing that it is a compactly
generated tensor triangulated category.