nLab coring spectrum




A coring spectrum is a comonoid object in the symmetric monoidal (infinity,1)-category of spectra. The concept of a coring spectrum is to that of a ring spectrum like a coalgebra is to an associative algebra.



(suspension spectra carry canonical structure of coring spectra)
Every \infty -groupoid (homotopy type of a topological space) XX is canonically a comonoid object in the Cartesian monoidal (infinity,1)-category ∞Grpd (here). Accordingly, since forming suspension spectra is strong monoidal (see there), its suspension spectrum Σ X +\Sigma^\infty X_+ is a coring spectrum (via the smash-monoidal diagonals).

For more on this coring structure on suspension spectra see also (here) at suspension spectrum and see discussion of A-theory as in Hess & Shipley 2014.


The canonical coring-spectrum structure on suspension spectra is used in

(for discussion of A-theory).

Last revised on August 25, 2023 at 16:09:40. See the history of this page for a list of all contributions to it.