Dear Sergey, Here is a simple example, based on the ordered class ORD of all ordinals numbers. The subclass LIMIT of all limit ordinals is reflexive in ORD. Let us denote by L the resulting reflection operator. Similarly, the subclass SUCC of all successor ordinals is reflexive in ORD. Let us denote by S the resulting reflection operator. The operators L and S cannot be bounded simultaneously by a reflection operator (= monad) since the classes LIMIT and SUCC have an empty intersection. Best, Andre -------- Message d'origine-------- De: Sergey Goncharov [mailto:sergey@informatik.uni-bremen.de] Date: mer. 28/07/2010 10:02 À: categories@mta.ca Objet : categories: Tensor of monads Dear categorists, in "Combining algebraic e?ects with continuations", by Hyland et al. the authors say carefully: "In general, the tensor product of two arbitrary monads seems not to exist.." without providing a counterexample though, presumably because they did not have any. Was there any progress reported on this issue since then? Or maybe someone can even make up a counterexample right on the nail? Thanks, -- Sergey Goncharov, Junior Researcher DFKI Bremen Phone: +49-421-218-64276 Safe and Secure Cognitive Systems Fax: +49-421-218-9864276 Cartesium, Enrique-Schmidt-Str. 5 Email: Sergey.Goncharov@dfki.de D-28359 Bremen Site: www.dfki.de/sks/staff/sergey [For admin and other information see: http://www.mta.ca/~cat-dist/ ]