POSTING TO CATNET

Date: Thu, 23 Mar 2006 09:06:08 -0500 (EST)

From: F W Lawvere wlawvere@buffalo.edu

Subject: George Mackey, 1916-2006

Dear friends,

Together with many others, I am deeply saddened by the death of George Mackey. For far too long, I had been delaying the trip to see him and continue our discussions which had started in the "Weyl'sche Kammer" at the ETH in Zurich and continued in the physics center in Trieste. Long before I met him, his insights into mathematics and into quantum mechanics had been informing my own thinking. It was the study of his book on quantum mechanics in 1967, which led directly to the joint course by Saunders Mac Lane and me at the University of Chicago. But his relation to category theory goes back much further than that, as Saunders and Sammy had explained to me.

George Mackey's Ph.D. thesis displayed remarkable thinking of a categorical nature, even before categories had been defined. Specifically, the fact that the category of Banach spaces and continuous linear maps is fully embedded into a category of pairings of abstract vector spaces, together with the definition and use of "Mackey convergence" of a sequence in a "bornological" vector space were discovered there and have played a basic role in some form in nearly every book on functional analysis since. What is perhaps unfortunately not clarified in nearly every book on functional analysis, is that these concepts are intensely categorical in character and that further enlightenment would result if they were so clarified. And who, despite initial skepticism, permitted the first paper giving an exposition of the theory of categories to see the light of day in the Transactions of the AMS in 1945? None other than the referee, George Whitelaw Mackey.

Sincerely,

F. William Lawvere