Homotopy Theory of Comodules over a Hopf Algebroid

  title={Homotopy Theory of Comodules over a Hopf Algebroid},
  author={Mark Hovey},
Given a good homology theory E and a topological space X, E∗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, Γ). That is, we construct the derived category Stable(Γ) of (A, Γ) as the homotopy category of a Quillen model structure on Ch(Γ), the category of unbounded chain complexes of Γ-comodules. This derived category is obtained by inverting the… CONTINUE READING