Dirk Hofmann - Departamento de Matem ́atica, Universidade de Aveiro, ۳۸۱۰-۱۹۳ Aveiro, Portugal.
Gavin J. Seal - Ecole Polytechnique F ́ed ́erale de Lausanne, Station ۸, CH-۱۰۱۵ Lausanne, Switzerland

In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

Monad, lax extension, quantale, enriched category