Derived categories in algebra and topology
by J.P. May
Abstract
An analogy between the derived category of modules over a
commutative ring and the stable homotopy category of spectra is elaborated
to a much closer analogy between the derived category of E infinity modules
over an E infinity algebra and the derived category of E infinity module spectra
over an E infinity ring spectrum. In both the algebraic and topological
contexts, these new derived categories allow one to study ``modules up to
homotopy'' over ``commutative algebras up to homotopy'' in much the same way
that one studies ordinary modules in classical homological algebra. There are
many applications in algebraic topology, algebraic K-theory, and algebraic
geometry. This expository note explains the ideas and gives a brief summary
of the relevant definitions in both contexts.
This paper will appear in the proceedings of the Eleventh International
Conference on Topology, Trieste, 1993.