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While the theory of higher categories was not developed in the time of Bourbaki, it seems that the nPOV is an extension of the BPOV of Bourbaki expressed in his paper The Architecture of Mathematics.
A lot of his examples are outdated and don't take into account much of category theory (remember, this was written in 1950), but overall, it seems like the nPOV takes the BPOV and extends it to newer fields. Although perhaps Bourbaki may have disagreed with certain parts of these extensions, it seems that his core philosophy of is still intact within the nPOV.
I was wondering what the rest of you think, just because it seems like an interesting discussion to have.
For the larger context of Bourbaki’s thinking, and its relation to category theory, I recommend Part 2 of Corry’s book Modern Algebra and the Rise of Mathematical Structures.
I have no expertise on these historical aspects, but my impression had been that Bourbaki had secretly emphasized that the mathematical structure you define shoud form a concrete category.
Bourbaki did not use any explicit category theory, I think, because they did not use classes (nor universes).
Bourbaki did not use any explicit category theory, I think,
Yes, but Bourbaki established the habit of precisely defining a mathematical structure as a set with certain structure and properties and homomorphisms between them as structure preserving morphisms.
This amounts to (implicitly) defining the concrete category of the mathematicl object in question.
I mean, N. Bourbaki wrote the chapter introducing universes in SGA4.
double post
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