categories: Vector lattices

[Jean-Pierre Cotton <cotton@ensae.fr>]

 Dear categorists
 I am interested in applications of category theory to probability , 
fuzzy sets and statistical theory.
 A useful concept is that of "probability hilbert spaces" (see the book
"Hilbert space methods in probability and statistical inference" by small 
and Mc Leish, Ed Wiley), that is Hilbert space with additional lattice
structure
and some compatibility betwen the two structures. This can be seen as a 
category, the morphisms are maps preserving both structures. This is 
also a particular case of more general structures , those of Banach 
lattices and Riesz spaces , which are vector spaces with lattice 
structure.
 Does anyone know if those kinds of structures have been studied from a
categorical point of view?
 Regards.

 J. P. Cotton.