It is with great sadness I write to let you know that our friend Aurelio Carboni died peacefully this morning, 11 December 2012.

We had been friends and collaborators since I first met him in 1980. I know that all of you who knew him personally will share my distress at his passing. We remember his friendship, his spirit, his humour and his passion for mathematical research.

It is a great loss to the Category Theory community.

Dear Colleagues,

We are so very sad that Aurelio is so unexpectedly gone. We will sorely miss his unique contributions to our community.

It seems only yesterday (but actually it is 40 years) since he, in Perugia, started to teach me his unique Italian with the same enthusiasm that he applied to learning category theory. I never ceased to admire his quick grasp of mathematics, and his clear perception of situations and characters.

My life (like the lives of many of us) was enriched by his commentaries both wry and profound, yet full of humor and kindness and warmth.

As all the friends, I am deeply distressed at saying goodbye to Aurelio.

I am one of many who will never forget Aurelio's talent and vision of mathematics, and his friendship and support.

The song has it that "only the good die young". Maybe not "only", but certainly "all too often".

May Aurelio rest in peace, and live on in his work and our memories.

Dear colleagues and friends,

This is quite a shock to me. I regret not having visited him when Bob (Walters) and Aurelio himself encouraged me to do so. There was so much I wanted to discuss with him. I will always remember Aurelio as a great collaborator for his kindness, mathematical insights, and humor. He was a good friend as well. My sabbatical in Genova was very special because of Marco, Pino, and Aurelio. My condolences to the categories group.

Indeed, a great loss. Men with intellectual honesty, integrity and mathematical talent like him are few in the Category Theory community. I compare him with another great loss we had, Max Kelly.

I worked with Aurelio in Milan for a month, about twenty years ago. The routine was that I would come in in the morning and try to understand what he had told me the day before, he would come rushing in just before lunch, we would go and eat, then do some work, go for an espresso, do more work, then go for drinks and supper. The next day the same thing. His ownspecial method of proof is summed up in his phrase "What else could be?" It worked well!

It was a wonderful time and I'm very sad I won't see him again.

I was not exactly a friend of Aurelio, but I will remember his support, his peculiar kindness and, as many others, also his talent and humour.

Io non ero esattamente un amico di Aurelio, ma ricorderò il suo appoggio, la sua particolare gentilezza e, come tanti altri, anche il suo talento e umorismo.

The disappearance of Aurelio leaves me sad. He was an exceptionnal person and a good mathematicians.

His motto may have been: Takes category theory seriously but dont take human been too seriously.

We will miss him.

Others have expressed well many of the sentiments I also feel. Aurelio and Patrizia were very kind to us. Our family loved travelling in his big Citroen and stopping off for delicious gelati on the way home from school.

We were a bit worried once, taking Aurelio to an Italian restaurant at Bondi Beach (Papa Giovanni's). Could be a disaster. We were served our pizzas and were hoeing in. We noticed some mild activity with Aurelio's hands involving putting his finger to his cheek and other things. Then Aurelio stood up. We asked where he was going. He said the chef had invited him to taste the spaghetti he himself was eating at another table. Not a word had been spoken.

So many memories, personal and mathematical.

It's true Aurelio is really a big loss, and we will all miss him. He was a wonderful person with a great sense of humour, and a fine category theorist. He was unique.

I miss him very much. Especially because doing mathematics with him was a lot of fun. His humor, his naturalness, his spontaneity were like a force of nature. And I was very lucky as I could receive his harsh criticisms directly in his mother language, and respond.

And I always remember with joy the very long night we spent together, when we met at 6pm EST at the gate of a flight from JFK to Denver; coming from different places across the Atlantic, each had missed his connecting flight. For a technical problem, we then sat at the gate for four hours waiting for a replacement aircraft. We got to Denver at 4am MST, arriving in Boulder at 7am in time for breakfast. Yet he made it the most absolutely delightful trip for me.

We were colleagues at Genoa, for a few years in 1993-96, and had a paper together on a matter of common interest but based on his initial idea and intuition. In that period, we had the pleasure of having Marta Bunge with us, during her sabbatical in 1993-94, as she already recalled in her message.

Then he moved back to Milano and later to Como, and I only met him at conferences and meetings. I regret we had no further occasions of working together.

I am shocked, as so many of his colleagues and friends.

This is really sad news. Aurelio was a unique person, merging mathematical insight, humour and one, his very own, disenchanted sense of life. The latter was a recurrent subject of debate between us every time we met, since the first time at the State University of Milan in 1983, during a seminar in logic. His remarks, in the form of criticism and suggestion on specific topics of research, were always helpful to grasp the point of a problem, seen from his own, deep, understanding of mathematics.

I am terribly sad and will miss Aurelio a lot.

The time we spent together was extraordinary and unforgettable!!

In 1994 in Tours at the Category Theory Conference Aurelio Carboni gave a talk. When he came to give the proof of his announced theorem he said in his inimitable way:

This caused a certain consternation in some sections of the audience, which I understood.

However the point I wish to make in this post is that Aurelio seems to have been wiser, and closer to my position, than those who now advocate the total formalization of mathematics and logic in some formal proof system, based on type theory.

Aurelio often said that the main problem is to get the definitions right.

A crucial problem of mathematics is to understand what is important and interesting, and what we learn about the world from it.

Incidentally, Aurelio was very interested in making mathematics of proof theory; not in making mathematics into type-theory pseudocode.

This is my recollection of my working with Aurelio in Genova. The outcome of this joint work was a jewel of a paper, called "The Symmetric Topos", and published in the JPPA. I can say that it is a jewel since, although I had proved elsewhere (Algebra Universalis) the original conjecture of Bill Lawvere to the effect that the symmetric topos exists as classifier of Lawvere distributions, the way of doing things in our joint paper has Aurelio's mark all over it. Instead of forcing (in the set-theoretic or topos-theoretic sense) the existence of the symmetric topos, as I had done, he suggested constructing it using the finite limits completion on the sites. This way of doing it unifies ring theory and topos theory. Bello! We had envisaged a sequel to our work, but that never happened.

Working with Aurelio was fun and terribly exciting. The fun came from the fact that we would work at odd places - during lunch, on an outing in his fast car, and even during his taking oral examinations at Universita di Genova. This was a far cry from my working in offices with previous collaborators. I found that, this way, we would concentrate on the ideas - leaving the details to be worked afterwards. His intuition (almost) never failed, so this sort of work was actually productive. Coming back to Aurelio, what I liked most about him was his frankness, but the same time his friendship, optimism, and encouragement.

My first recollection of Aurelio was at a workshop on Categorical Methods in Geometry at Aarhus, organized by Anders Kock. Aurelio was young, eager, more serious than what he later became. Maybe Anders has a picture of young Aurelio listening attentively to Bill Lawvere in the garden of his house. In another photograph, we are at lunch in the same garden, with Aurelio sitting on my left, talking across the table to Gavin Wraith, Imogen Kelly and Andy Pitts. I looked very young myself, so it must have been at least about 20 years ago. I do not remember dates , but I could check on all the ones that are missing from this account. I could also look for the photographs that I mentioned.

For now, what I have are the memories of the many meetings in which I talked to Aurelio. At CT 2010, I asked Bob Walters what was the matter with Aurelio since he was not there (Calais) and that was not at all like him. I asked Bob if in fact Aurelio was ill. The response was that it was "worse" - that what happened was that he was "disappointed". Well, as it turned out, he was, or must have been ill already then, and nobody noticed it. I could not believe that Aurelio was in any way depressed but asked no more. I said to Bob that I would like to see Aurelio, and he told this to Aurelio, who encouraged me to go visit him. As it usually happens, I am not that free to plan my travels, so I did not. I am so very very sorry that I did not. If only time could go backwards... .