In reply to the query of Jean-Pierre Cotton, I would like to mention the following: In Springer LNM 915 (1982), an article by Michele Giry develops some aspects of "A categorical approach to probability theory".The key idea, which also was discussed in an unpublished 1962 paper of mine, is that random maps between spaces are just maps in a category of convex spaces between "simplices". There is a natural (semi) metric on the homs which permits measuring the failure of diagrams to commute precisely, suggesting statistical criteria. To make full use of the monoidal closed structure,as well as to account for convex constraints on random maps,it seems promising to consider also nonsimplices. (Noncategories is usually not a good idea). The central observation that the metrizing process is actually a monoidal functor was exploited in the unpublished doctoral thesis here at Buffalo by X-Q Meng a few years ago in order to clarify statistical decision procedures and stochastic processes as diagrams in a basic convexity category. She can be reached at : meng@lmc.edu Best wishes to those interested in pursuing this topic! Bill Lawvere ******************************************************************************* F. William Lawvere Mathematics Dept. SUNY wlawvere@acsu.buffalo.edu 106 Diefendorf Hall 716-829-2144 ext. 117 Buffalo, N.Y. 14214, USA ******************************************************************************* On Tue, 20 Oct 1998, jean-pierre-C. wrote:
Bonjour. I am a statistician and I should be interested in a categorical framework for probability and statistical theory. Does anyone know references (books, articles, websites...) about applications of categories and functors to probability or even measure theory ? Thank you.
Very truly yours,
Jean-Pierre Cotton.