Re: Bourbaki and Categories

[Andree Ehresmann <andree.ehresmann@u-picardie.fr>]

  Dear all,

I would add some information on Bourbaki/categories/France.
Charles Ehresmann has been an active member of Bourbaki from 1936 up  
to the end of the war, when he began to no more regularly participate  
and wanted to resign (it was not accepted but replaced by an age limit  
for active participation).
What Andre says:

    >Bourbaki had essentially two options: rewrite the whole treaty using
    > categories, or just introduce them in the book on homological algebra,
    >The second option won, essentially because of the enormity of the task
    > of rewriting everything.

is more easily understood if we take into account that communication  
between France and the USA were entirely broken during the war, so  
that mathematical ideas could not circulate and categories were only  
heard of after the war, at a time where the more general parts of the  
treatise were written or at least prepared (the successive versions  
process was very slow).
     Charles said to me that he did not recall to have read Eilenberg  
& Mac Lane's paper before the fifties, or at least not seen its  
interest. Naturally he had sooner made a large use of groupoids in is  
foundation of differential geometry, and he had even defined the  
general "composition of jets" and given its properties, but without  
linking it to the notion of a category. He exposed it in a course in  
Rio de Janeiro in the early fifties, and one of his students  
(Constantino de Barros who later came to Paris to prepare a thesis  
with him) suggested that there was a connection with categories.  
Charles' first large use of categories is in his seminal paper  
"Gattungen von lokalen Strukturen" (1957, reprinted in "Charles  
Ehresmann: Oeuvres completes et commentees" Part I).
    It is around this date that the word "category" began to circulate  
in France.  In 1957, Choquet  (with whom I prepared my thesis)  
suggested that I learnt more on the notion of category which he did  
not know but seemed to have many applications (it was the reason for  
which I first went to see Charles!). It should be noted that Choquet  
was less conservative than many French mathematicians. In 1959, he  
defended the development of probabilities by inviting Loomis to give a  
course (I remember Henri Cartan saying then to Paul-Andre Meyer that  
he should not study this domain for it would be bad for his career!).  
And later on, he defended Logic which was very badly considered.
    A final remark: the "disdain" for categories (not to be confused  
with 'ignorance') came only later on, since Charles was given the  
"Prix Petit d'Ormoy" by the French Academy in 1965, essentially for  
his recent work on categories...

Andree C. Ehresmann