Tensor of monads

["Joyal, André" <joyal.andre@uqam.ca>]

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


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