Geodesic
Enriched Lawvere theories
Theory and applications of categories, The Lambek Festschrift, Tome 6 (1999), pp. 83-93

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18C10, 18C15, 18D05.
Keywords: Lawvere theory, monad. 
@article{TAC_1999_6_a6,
     author = {John Power},
     title = {Enriched {Lawvere} theories},
     journal = {Theory and applications of categories},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {6},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_1999_6_a6/}
}
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John Power. Enriched Lawvere theories. Theory and applications of categories, The Lambek Festschrift, Tome 6 (1999), pp. 83-93. http://geodesic.mathdoc.fr/item/TAC_1999_6_a6/