symmetric monoidal (∞,1)-category of spectra
equivalences in/of $(\infty,1)$-categories
The notion of monoid (or monoid object, algebra, algebra object) in a monoidal (infinity,1)-category $C$ is the (infinity,1)-categorical generalization of monoid in a monoidal category.
For $C$ a monoidal (∞,1)-category with monoidal structure determined by the (∞,1)-functor
a monoid object of $C$ is a lax monoidal (∞,1)-functor?
This generalizes how, for monoidal categories, monoid objects are the same as lax monoidal functors
definition 1.1.14 in
An equivalent reformulation of commutative monoids in terms (∞,1)-algebraic theories is in