Contents

# Contents

## Idea

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.

## Examples

###### Example

(suspension spectra carry canonical structure of coring spectra)
Every $\infty$-groupoid (homotopy type of a topological space) is canonically a coalgebra object? in the Cartesian monoidal (infinity,1)-category ∞Grpd (here). Accordingly, since forming suspension spectra is strong monoidal, its suspension spectrum $\Sigma^\infty X_+$ is a coring spectrum.

For more on this coring structure on suspension spectra see also discussion of A-theory as in Hess & Shipley 2014.

## References

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

(for discussion of A-theory).

Last revised on August 21, 2022 at 14:47:37. See the history of this page for a list of all contributions to it.