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) $X$ 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 $\Sigma^\infty X_+$ 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

- Kathryn Hess, Brooke Shipley,
*Waldhausen K-theory of spaces via comodules*, Advances in Mathematics 290 (2016): 1079-1137 [arXiv:1402.4719, doi:10.1016/j.aim.2015.12.019]

(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.