symmetric monoidal (∞,1)-category of spectra
An $E_\infty$-algebra is an algebra over an operad for an E-∞ operad.
$E_\infty$-algebras in chain complexes are equivalent to those in abelian simplicial group.
For details on this statement see monoidal Dold-Kan correspondence and operadic Dold-Kan correspondence.
A connected space of the homotopy type of a CW-complex with a non-degenrate basepoint that has the homotopy type of a $k$-fold loop space for all $k \in \mathbb{N}$ admits the structure of an $E_\infty$-space.
The model structure on algebras over an operad over E-∞ operads in Top and in sSet are Quillen equivalent.
This is in BergerMoerdijk I, BergerMoerdijk II.
An $E_\infty$-algebra in spectra is an E-∞ ring.
See Ek-Algebras.
See symmetric monoidal (∞,n)-category.
In the context of (infinity,1)-operads $E_\infty$-algebras are discussed in
A systematic study of model category structures on operads and their algebras is in
The induced model structures and their properties on algebras over operads are discussed in