  In this paper, we present an infinity-categorical version of the theory of
monoidal categories. We show that the infinity category of spectra admits an
essentially unique monoidal structure (such that the tensor product preserves
colimits in each variable), and thereby recover the classical smash-product
operation on spectra. We develop a general theory of algebras in a monoidal
infinity category, which we use to (re)prove some basic results in the theory
of associative ring spectra. We also develop an infinity-categorical theory of
monads, and prove a version of the Barr-Beck theorem.
