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

From: F W Lawvere <>


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.