The pairing of the concepts of commutative Hopf algebra and E-∞ algebra: the formal dual of a spectral group scheme, that is, a group scheme in E-∞ geometry.

- Jacob Lurie, def. 3.9.7 of Elliptic Cohomology I, (pdf)

Hopf (semi-)ring structure on the symmetric algebra of the sphere spectrum is discussed in

- Neil Strickland, Paul Turner,
*Rational Morava $E$-theory and $D S^0$*, Topology Volume 36, Issue 1, January 1997, Pages 137-151 (pdf)

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