  We consider the equivalence of Lawvere theories and finitary monads on Set
from the perspective of Endf(Set)-enriched category theory, where Endf(Set) is
the category of finitary endofunctors of Set. We identify finitary monads with
one-object Endf(Set)-categories, and ordinary categories admitting finite
powers (i.e., n-fold products of each object with itself) with
Endf(Set)-categories admitting a certain class Phi of absolute colimits; we
then show that, from this perspective, the passage from a finitary monad to the
associated Lawvere theory is given by completion under Phi-colimits. We also
account for other phenomena from the enriched viewpoint: the equivalence of the
algebras for a finitary monad with the models of the corresponding Lawvere
theory; the functorial semantics in arbitrary categories with finite powers;
and the existence of left adjoints to algebraic functors.
