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- W2951657345 abstract "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." @default.
- W2951657345 created "2019-06-27" @default.
- W2951657345 creator A5045461807 @default.
- W2951657345 date "2013-07-11" @default.
- W2951657345 modified "2023-09-27" @default.
- W2951657345 title "Lawvere theories, finitary monads and Cauchy-completion" @default.
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