Symmetric spectrum

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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 (with respect to smash product). 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.