  We adapt the notion of an algebraic theory to work in the setting of
quasicategories developed recently by Joyal and Lurie. We develop the general
theory at some length.
  We study one extended example in detail: the theory of commutative monoids
(which turns out to be essentially just a 2-category). This gives a
straightforward, combinatorially explicit, and instructive notion of a
commutative monoid. We prove that this definition is equivalent (in appropriate
senses) both to the classical concept of an E-infinity monoid and to Lurie's
concept of a commutative algebra object.

Algebraic Topology;Category Theory