The n-Category Café

I’ve always assumed the “gr” in “gr-category” was “group”. Is it?

I have Gavin Wraith’s blessing to pass on the following wonderful anecdote about Alexandru Solian, who wrote the first paper I’ve found that mentions categorical groups. I think such anecdotes deserve not to be forgotten.

In 1974 I was a visiting Professor at SUNY in Buffalo, and I lent my flat in Brighton, UK, to Bucur who was visiting Sussex University as a guest of Prof. Bernard Scott, our head of department. Perhaps as a consequence, I was sent by the British Council on a visit to Romania in 1977, to the universities of Bucharest and Cluj-Napoca, to report on the state of mathematics in Romania. One of the people I met in Bucharest was Prof. Solian. You have to understand that at that time Romania was under the thumb of the Ceaucescu regime. Bucur was not allowed to meet foreigners like myself because his student, Diaconescu, had defected. I was supposed to be escorted by a ‘party member’ wherever I went, to see that I did not get up to mischief. In fact I did talk to Bucur, in an empty lecture theatre, while the ‘party member’s attention was diverted by a friend who was a mathematical, as opposed to a political, member of the mathematics department. But we only talked mathematics. The paranoia was absurd and pointless, of course. Solian, who had no students to defect, was allowed to talk to me. Moreover, he had an elderly mother to care for, which kept him chained to Romania, so his desire for travel and meeting foreign mathematicians could not be satisfied.

In 1978 I was invited to give a talk at the ICM in Helsinki. Solian was there ( his mother had died), in a group of Romanian mathematicians who had been allowed out after Ceaucescu’s daughter, who was studying for a degree in mathematics, had begged her mother to let them go. They were not allowed to take any money. They were issued with meal tickets and had to stay in a group.

I was approached by a French mathematician who asked if I would help Solian to defect, and I said I would. The problem was that telephone calls from Helsinki were monitored by the Russians, who would probably pass on relevant information to the Romanians. He would arrange for a ticket on a boat from Helsinki to Stockholm if I would get Solian onto the boat. The Wednesday afternoon was ‘outing day’.

Solian feigned illness while the rest of his group was escorted on a tour of the islands. I took Solian on a walk in the cemetery, where we were less likely to be spotted. He was very nervous. Eventually I got him onto the boat. I never saw him again.

I later heard that after the boat had sailed Solian had met Foias, Miss Ceaucescu’s thesis adviser, in the lounge. Each of the two men thought the other had been sent to spy on them!

Excuse me burdening you with this tale. The Ceaucescus are gone. Romania is a different place now. In fact my half-brother is married to a Romanian, and their daughter is happily studying in the USA.

— Best wishes, Gavin Wraith

Maybe the term “categorical group” has been used to mean (weak) 2-group from the beginning. I mean, the first actual use of the term you have found is by A. Solian, 1981. Why should we suspect that this terminology was used before to mean strict 2-group?