Re: Bourbaki and category theory again

[William Messing <messing@math.umn.edu>]

Concerning Borceaux's citation of "Revised and reduced..." in the second 
edition of Bourbaki, Theorie des Ensembles, chapitre IV, I think a more 
accurate translation is "suppressed", rather than "reduced".  What was 
suppressed from the first, 1957, edition of Structures was the 19 page 
appendix, titled Criteres de transportabilite, and  devoted to giving 
useful criteria for verifying that a relation of a theory T, is 
transportable relative to a given typification, as these terms are 
defined in ¶ 1 of this chapter.  Thus, this appendix   also explains the 
concept of "transport of structure", a notion that Bourbaki employed 
frequently and also gives a rigorous definition of "canonical". 

It seems plausible that Chevalley was the author of this appendix, 
although Bourbaki tradition is to not confirm or deny such a statement.

I have never understood why Bourbaki chose to suppress this appendix, as 
I find it very interesting  and very well written.

Bill Messing


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