Recent investigations of lax algebras - in generalization of Barr's relational algebras -make an essential use of lax extensions of monad functors on Set to the category Rel(V) of sets and V-relations (where V is a unital quantale). For a given monad there may be many such lax extensions, and different constructions appear in the literature. The aim of this article is to shed a unifying light on these lax extensions, and present a symptomatic situation in which distinct monads yield isomorphic categories of lax algebras.
Keywords: lax algebra, Kleisli extension, initial extension, strata extension, tower extension
2000 MSC: 18C20, 18B30, 54A05
Theory and Applications of Categories,
Vol. 21, 2008,
No. 7, pp 118-151.
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