symmetric monoidal (∞,1)-category of spectra
Recall the pattern in ordinary algebra:
Accordingly in higher algebra:
In a symmetric monoidal (infinity,1)-category one can consider commutative algebra objects.
A commutative algebra object in a symmetric monoidal (infinity,1)-category is a lax symmetric monoidal -functor
* \to C \,.
In more detail, this means the following:
p : C^\otimes \to N(FinSet_*)
a commutative algebra object in is a section
A : N(FinSet_*) \to C^\otimes
such that carries collapsing morphisms in to coCartesian morphisms in .
the above definition is definition 1.19 in