Symmetric spectrum
In algebraic topology, a symmetric spectrum X is a spectrum of pointed simplicial sets that comes with an action of the symmetric group on 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.
The technical advantage of the category of symmetric spectra is that it has a closed symmetric monoidal structure. It is also a simplicial model category. A symmetric ring spectrum is a monoid in ; if the monoid is commutative, it's a commutative ring spectrum. The possibility of this definition of "ring spectrum" was one of motivations behind the category.
A similar technical goal is also achieved by May's theory of S-modules, a competing theory.
