CATNET POSTING ABOUT JON BECK

Date: Thu, 23 Mar 2006 10:56:34 -0500 (EST)

From: F W Lawvere <wlawvere@buffalo.edu>

To: categories@mta.ca

Subject: Jon Beck

Dear Friends,

It is happening much too often
during this past year. Discussions, whose continuation has been too long
delayed, are forever ended by the sad passing of a colleague. Particularly
poignant for me is the loss of my friend and collaborator from Varenna and the
ETH in 1966 and in the Zurich Triples book (SLNM No. 80). Beyond his famous and
far-reaching results on tripleability, intensive discussions with Jon led to
some of the points raised in my paper in that book.

The word "doctrine" itself is entirely due to him
and signifies something which is like a theory, except appropriate to be
interpreted in the category of categories, rather than, for example, in the
category of sets; of course, an important example of a doctrine is a 2-monad,
and among 2-monads there are key examples whose category of
"algebras" is actually a category of theories in the set-interpretable
sense. Among such "theories of theories", there is a special kind
whose study I proposed in that paper. This kind has come to be known as
"Kock-Zoeberlein" doctrine in honor of those who first worked out
some of the basic properties and ramifications, but the recognition of its
probable importance had emerged from those discussions with Jon.

In those days Jon was insistent on mathematical clarity and
did much to encourage precision in discussions and in the formulation of
mathematical results.

We lovingly remember him from those youthful days.

Bill