symmetric monoidal (∞,1)-category of spectra
Dual to the concept of a module spectrum over a ring spectrum is a comodule spectrum over a coring spectrum, the analog in stable homotopy theory of the concept of comodules in algebra and homological algebra.
The suspension spectrum of any ∞-groupoid (homotopy type of a topological space) is canonically a coring spectrum by the fact that every , is uniquely a coalgebra object? in the Cartesian monoidal (∞,1)-category ∞Grpd via the diagonal (here), and using that is a strong monoidal functor.
If is connected object in an (∞,1)-topos (the homotopy type of a connected topological space) then -comodule spectra are equivalently module spectra over the ∞-group ∞-ring of the loop space ∞-group of .
(Hess-Shipley 14, theorem 1.2 with prop. 5.18)
See also at A-theory.
Last revised on March 7, 2017 at 19:35:23. See the history of this page for a list of all contributions to it.