nLab commutative ring spectrum

Context

Higher algebra

higher algebra

universal algebra

Theorems

Stable Homotopy theory

stable homotopy theory

Contents

Idea

An ordinary (commutative) ring is a (commutative) monoid or algebra object internal to the symmetric monoidal category Ab of abelian groups.

The role that Ab plays among ordinary categories is played by the stable (infinity,1)-category of spectra $Sp$ among (infinity,1)-categories.

A commutative ring spectrum, or E-infinity ring, is accordingly a commutative algebra in an (infinity,1)-category.

Definition

A commutative ring spectrum is a commutative algebra object in the symmetric monoidal (infinity,1)-category of spectra.

References

reference to standard literature on $E_\infty$ things goes here …

then..

the $(\infty,1)$-categorical perspective on commutative ring spectra is the topic of

section 7 of

Revised on October 27, 2011 20:23:27 by Urs Schreiber (131.174.189.40)