Duality à la Bourbaki

In this chapter, we will investigate an aspect in the post-1930 history of duality which deserves special attention, namely the influence of Bourbaki. More precisely, we will inspect various occurences of duality in Bourbaki’s activities, mostly in the time period from the founding of the group in 1934 to the appearance of the chapter on linear algebra in 1947 (we will explain in 14.2 why our focus is on this chapter in particular). During that period, several founding members of the group, and some members of the second generation, contributed in essential ways to the development of duality, and the internal discussion of the group concerning the preparation of their collective work also dealt with issues of duality. This said, we should stress from the beginning that in our opinion the mutual relation of Bourbaki and duality should not be overstated: our claim is neither that Bourbaki was crucial for duality nor the other way round. Our claim is a somewhat more modest one, namely that a focus on duality provides new insights in Bourbaki’s history, and a focus on Bourbaki provides new insights in the development of duality.