#
Enriched Lawvere theories

##
John Power

We define the notion of enriched Lawvere theory, for enrichment over a
monoidal biclosed category $V$ that is locally finitely presentable as
a closed category. We prove that the category of enriched Lawvere
theories is equivalent to the category of finitary monads on $V$.
Moreover, the $V$-category of models of a Lawvere $V$-theory is
equivalent to the $V$-category of algebras for the corresponding
$V$-monad. This all extends routinely to local presentability with
respect to any regular cardinal. We finally consider the special case
where $V$ is $Cat$, and explain how the correspondence extends to
pseudo maps of algebras.

Keywords: Lawvere theory, monad.

1991 MSC: 18C10, 18C15, 18D05.

*Theory and Applications of Categories*, Vol. 6, 1999, No. 7, pp 83-93.

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