Subject: categories: Jon Beck

From: F W Lawvere <[email-masked]>
Date: Thu, 23 Mar 2006 10:56:34 -0500 (EST)

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

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F. William Lawvere
Mathematics Department, State University of New York
244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
Tel. 716-645-6284
HOMEPAGE:  http://www.acsu.buffalo.edu/~wlawvere
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