QUESTION

They had plenty of time to adopt the theory of categories. They had Eilenberg, then Cartan, then Grothendieck. Did they feel that they have established their approach already, that it's too late to go back and start anew?

I have my very-very general answer: World is Chaos, Mathematics is a Jungle, Bourbaki was a nice fluke, but no fluke can last forever, no fluke can overtake Chaos and Jungle. I'd still like to have a much more complete picture.

Appendix: CHRONOLOGY

• 1934:   Bourbaki's birth (approximate date);
• 1942-45:   Samuel Eilenberg & Saunders Mac Lane - functor, natural transformation, $K(\pi,n)$;
• 1946 & 1952: S.Eilenberg & Norman E. Steenrod publish "Axiomatic..." & "Foundations...";
• 1956: Henri Cartan & S.Eilenberg publish "Homological Algebra";
• 1957: Alexander Grothendieck publishes his "Tohoku paper", abelian category.

(*Feel free to add the relevant most important dates to the list above*).