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 formula_1 on formula_2 such that the composition of structure maps
is equivariant with respect to formula_4. 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 formula_5 of symmetric spectra is that it has a closed symmetric monoidal structure (with respect to smash product). It is also a simplicial model category. A symmetric ring spectrum is a monoid in formula_5; 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.