In algebraic topology, a symmetric spectrum X is a spectrum of pointed simplicial sets that comes with an action of the symmetric group
such that the composition of structure maps is equivariant with respect to
A morphism between symmetric spectra is a morphism of spectra that is equivariant with respect to the actions of symmetric groups.
A symmetric ring spectrum is a monoid in
The possibility of this definition of "ring spectrum" was one of motivations behind the category.