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.
Theory and Applications of Categories, Vol. 6, 1999, No. 7, pp 83-93 http://www.tac.mta.ca/tac/volumes/6/n7/n7.dvi http://www.tac.mta.ca/tac/volumes/6/n7/n7.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/6/n7/n7.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/6/n7/n7.psTAC Home