Symmetric spectrum

Summary

A symmetric spectrum is a spectrum in which the $n$-th space carries an action of the symmetric group on $n$ letters. These actions are compatible with the structure maps. This extra symmetry gives a smash product of spectra that is associative, commutative and unital on the nose, not only up to homotopy. Symmetric spectra form a model for the stable homotopy category in which ring spectra with fully coherent multiplications are simply monoids.