TY - JOUR ID - 10709 TI - A cottage industry of lax extensions JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Hofmann, Dirk AU - Seal, Gavin J. AD - Departamento de Matem ́atica, Universidade de Aveiro, 3810-193 Aveiro, Portugal. AD - Ecole Polytechnique F ́ed ́erale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland Y1 - 2015 PY - 2015 VL - 3 IS - 1 SP - 113 EP - 151 KW - Monad KW - lax extension KW - quantale KW - enriched category DO - N2 - 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. UR - https://cgasa.sbu.ac.ir/article_10709.html L1 - https://cgasa.sbu.ac.ir/article_10709_6dda525bdadbecfac60152d5865b84f9.pdf ER -