Skip to main content
added 147 characters in body
Source Link
user44143
user44143

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article Saunder Mac Lane as Philosopher of MathematicsThe Last Mathematician from Hilbert’s Gottingen: Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".


Edit: Although the thread has closed and quid (user9072) has departed, Francois Ziegler recently brought to my attention in a comment below that Ralf Krömer (2006; pdf) (subtitled Bourbaki and categories during the 1950s) has thoroughly investigated the OP’s question, using unpublished internal reports of the meetings of Bourbaki, as well as correspondence and quotes of e.g. Eilenberg (p. 142), Cartier (p. 147), Grothendieck (p. 149), and others. There is quite a rich treasure trove of well-sourced information there, for those who are interested.

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".


Edit: Although the thread has closed and quid (user9072) has departed, Francois Ziegler recently brought to my attention in a comment below that Ralf Krömer (2006; pdf) (subtitled Bourbaki and categories during the 1950s) has thoroughly investigated the OP’s question, using unpublished internal reports of the meetings of Bourbaki, as well as correspondence and quotes of e.g. Eilenberg (p. 142), Cartier (p. 147), Grothendieck (p. 149), and others. There is quite a rich treasure trove of well-sourced information there, for those who are interested.

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article The Last Mathematician from Hilbert’s Gottingen: Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".


Edit: Although the thread has closed and quid (user9072) has departed, Francois Ziegler recently brought to my attention in a comment below that Ralf Krömer (2006; pdf) (subtitled Bourbaki and categories during the 1950s) has thoroughly investigated the OP’s question, using unpublished internal reports of the meetings of Bourbaki, as well as correspondence and quotes of e.g. Eilenberg (p. 142), Cartier (p. 147), Grothendieck (p. 149), and others. There is quite a rich treasure trove of well-sourced information there, for those who are interested.

Post Made Community Wiki by Todd Trimble
added the references kindly supplied by Francois Ziegler
Source Link
Todd Trimble
  • 53.3k
  • 6
  • 205
  • 322

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".


Edit: Although the thread has closed and quid (user9072) has departed, Francois Ziegler recently brought to my attention in a comment below that Ralf Krömer (2006; pdf) (subtitled Bourbaki and categories during the 1950s) has thoroughly investigated the OP’s question, using unpublished internal reports of the meetings of Bourbaki, as well as correspondence and quotes of e.g. Eilenberg (p. 142), Cartier (p. 147), Grothendieck (p. 149), and others. There is quite a rich treasure trove of well-sourced information there, for those who are interested.

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".


Edit: Although the thread has closed and quid (user9072) has departed, Francois Ziegler recently brought to my attention in a comment below that Ralf Krömer (2006; pdf) (subtitled Bourbaki and categories during the 1950s) has thoroughly investigated the OP’s question, using unpublished internal reports of the meetings of Bourbaki, as well as correspondence and quotes of e.g. Eilenberg (p. 142), Cartier (p. 147), Grothendieck (p. 149), and others. There is quite a rich treasure trove of well-sourced information there, for those who are interested.

Source Link
Todd Trimble
  • 53.3k
  • 6
  • 205
  • 322

As mentioned in a comment, there are some people such as Colin McLarty who I think could give an informed answer. I am not one of those persons, but since this question is likely to be closed soon, I will just mention a few helpful references.

One is McLarty's article Saunder Mac Lane as Philosopher of Mathematics. Indeed the members of Bourbaki invited Mac Lane to speak to them, but it probably wasn't Mac Lane's French that was the problem in getting them to incorporate category theory into the grand vision. Mac Lane and Weil were of course colleagues at the University of Chicago and presumably had ample opportunity to discuss category theory (in English); as quoted in McLarty's article, Weil writes to fellow Bourbakiste Chevalley in 1951:

As you know, my honourable colleague Mac Lane maintains every notion of structure necessarily brings with it a notion of homomorphism, which consists of indicating, for each of the data that make up the structure, which ones behave covariantly and which contravariantly [...] what do you think we can gain from this kind of consideration?

McLarty explains in his article that Weil didn't understand Mac Lane. If I understand correctly, there were indeed opportunities to incorporate category theory within the Élements, specifically as part of an account of an abstract theory of structures, but (McLarty, page 5):

After the war, Bourbaki hotly debated how to make a working theory. All agreed it must include morphisms. Members Cartier, Chevalley, Eilenberg, and Grothendieck championed categories, as did their visitor Mac Lane. But Weil was a majority of one in the group, so they created a theory with structure preserving functions as morphisms (Bourbaki [1958]). They never used it, and not for lack of trying.

Throughout the discussion of Bourbaki's (or Weil's) attitude toward categories, McLarty mentions the work of Leo Corry, who discusses Bourbaki's structures in his book Modern Algebra and the Rise of Mathematical Structures (reviewed here). Related is a useful online article by Corry, published in Synthese, here. I won't attempt to summarize it, but there is discussion, on the basis of documents, of "the interaction between Bourbaki's work and the first stages of category theory".