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