  We survey Lawvere theories at the level of infinity categories, as an
alternative framework for higher algebra (rather than infinity operads). From a
pedagogical perspective, they make many key definitions and constructions less
technical. They are also better-suited than operads for equivariant homotopy
theory and its relatives.
  Our main result establishes a universal property for the infinity category of
Lawvere theories, which completely characterizes the relationship between a
Lawvere theory and its infinity category of models. Many familiar properties of
Lawvere theories follow directly.
  As a consequence, we prove that the Burnside category is a classifying object
for additive categories, as promised in an earlier paper, and as part of a more
general correspondence between enriched Lawvere theories and module Lawvere
theories.
