Geodesic
Extensions in the theory of lax algebras
Theory and applications of categories, The Tholen Festschrift, Tome 21 (2008), pp. 118-151.

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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.
Classification : 18C20, 18B30, 54A05
Keywords: lax algebra, Kleisli extension, initial extension, strata extension, tower extension 
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     author = {Christoph Schubert and Gavin J. Seal},
     title = {Extensions in the theory of lax algebras},
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Christoph Schubert; Gavin J. Seal. Extensions in the theory of lax algebras. Theory and applications of categories, The Tholen Festschrift, Tome 21 (2008), pp. 118-151. http://geodesic.mathdoc.fr/item/TAC_2008_21_a6/