categories: Bill Lawvere

["Jirí Adámek" <j.adamek@tu-bs.de>]

I am very sad that Bill Lawevere, a great mathematician and a great man,
has passed away. Jiri Rosicky and I had the extraordinary good luck of
working on several joint articles with Bill, and we have very happy memories
of that collaboration. It started after the publication of our book on
locally presentable categories in 1994: Bill approached us shortly after
that with the suggestion to study what properties make locally presentable
'tick'. We had difficuties understanding his suggestion, and during the
discussions about that we have realized that nobody had studied the
algebraic duality that would be the analogy of the Gabriel-Umer duality to
finitary varieties. This led to our first short joint paper.

Later Bill came with the suggestion to have a look at 'how algebraic
is algebra': is there a higher-order monad whose algebras are finitary
varieties? In one of his early mails on that topic he wrote that the
answer would probably depend on Ulam cardinals. (A concept we two had
not heard of before.) We spent months of intensive work on this topic
during which Bill's impulses were the much needed support in times when
there seemed to be no light at the end of the tunnel. But eventually
light came, and we published two joint papers, about varieties and about
locally finitely presentable categories. One of our basic results needed
the assumption of non-existence of measurable cardinals. Only then did
we two learned that they are also called Ulam cardinals- our admiration
for Bill's insight could not have been greater...

One day Bill came with the grand idea of a initiating a collection of
monographs on topics he found important. At first a group of enthusiastic
colleagues agreed to start working on the project, but as time went on,
one after another decided to quit. In the end, just one monograph was
realized, the joint book with Jiri Rosicky and Enrico Vitale on algebraic
theories. Bill  followed our work on it closely, supporting us and
criticizing what he did not find right. We were proud when he agreed to
write a preface to it.

During all the time of our collaboration with Bill he was extremely
patient and friendly. It is indeed a very  sad news that this great and
kind man has passed away.

Jiri Adamek


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