symmetric monoidal (∞,1)-category of spectra
is the category of commutative rings and ring homomorphisms.
A commutative ring is a commutative monoid object in Ab, so . As for commutative monoid objects in any symmetric monoidal category, the tensor product of commutative rings is again a commutative ring, and is the coproduct in ; thus is cocartesian monoidal.
There is a “smooth” version of : the category of smooth loci,