Dear Staffan, Bourbaki has laid the set theory-based foundations for the Elements of Mathematics in Théorie des ensembles Résumé in late 1930s, and when category theory has matured as an alternative foundation for mathematics they decided that it was too late for them to change horses in the midstream. Their time was limited and they had to scale down the original set-theoretical project several times anyway. Refer to A. Borel's article "Twenty-Five Years with Nicolas Bourbaki, (1949 – 1973)" for more detail. Mac Lane hints that there may have been other reasons as well: "Categorical ideas might well have fitted in with the general program of Nicolas Bourbaki for the systematic presentation of mathematics. However, his first volume on the notion of mathematical structure was prepared in 1939 before the advent of categories. It chanced to use instead an elaborate notion of an dchelle de structure which has proved too complex to be useful. Apparently as a result, Bourbaki never took to category theory. At one time, in 1954, I was invited to attend one of the private meetings of Bourbaki, perhaps in the expectation that I might advocate such matters. However, my facility in the French language was not sufficient to categorize Bourbaki. Perhaps the explanation for his resistance is the hard fact that categories were not made in France. Even Eilenberg's later membership in Bourbaki did not serve to overcome Bourbaki's disinclination. It may be that the circulation of new ideas is not always unhindered." (Applied Categorical Structures, Vol. 4, No. 2-3 (1996), 129-136) Comparing my copies of old editions of Bourbaki with latest editions, I see that he nevertheless sneaks categorical language here and there without, however, calling it explicitly category theory. Max
On 21/05/12 19:49, Staffan Angere wrote:
Dear categorists,
and also, hello everyone, since this is my first post here! I'm wondering about the connection of Bourbaki to category theory. The copy of "Theory of Sets" that I have says it's written in 1970. Yet, Dieudonné famously saiid that the theory of functors subsumed Bourbaki's theory of structures... and, also, Bourbaki's theory of structures is very clearly a theory of a type of concrete categories. On the other hand, I've seen claims that the categorists' use of "morphism" comes from Bourbaki. So who was first? Does anyone here know when Bourbaki's theory of structures was really conceived? I guess this might be self-evident to anyone born during the 1st half of the 20th century, but it has turned out to be really hard to find out for me.
Thanks in advance, staffan
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