Commutative ring spectrum

In algebraic topology, a commutative ring spectrum, roughly equivalent to a

of rational numbers is Quillen equivalent to the category of differential graded algebras over

Example: The Witten genus may be realized as a morphism of commutative ring spectra MString →tmf.

Almost all reasonable categories of commutative ring spectra can be shown to be Quillen equivalent to each other.

[citation needed] Thus, from the point view of the stable homotopy theory, the term "commutative ring spectrum" may be used as a synonymous to an