Dear colleagues. I had the same conjecture as Zoran : first category, second category … Best Jorge Sent from Gmail Mobile On Mon, 10 Jun 2024 at 11:14 Zoran Škoda <zskoda@gmail.com> wrote:
Dear colleagues,
I was also confused (many years ago) with this passage in Ulam's memoirs, but later have convinced myself that the confusion is purely terminological. When Ulam refers to category theory he likely means the notion of Baire's category and related theorems. Kuratowski-Ulam theorem and a few of other related results with Ulam's contribution to this field show that he was interested in this problematics in his early research phase.
It might be that my conclusion is not definitive but it looks at least very plausible.
Zoran Škoda
pon, 10. lip 2024. 14:28 Colin McLarty <colin.mclarty@case.edu> je napisao:
I have looked into this a good bit, without finding any documentary sources. I think those people are right, who have suggested that Ulam and others had used specific examples of functors and natural transformations without stating any general concept of them. But of course lots of people did that long before Ulam or Eilenberg-Mac Lane.
On Mon, Jun 10, 2024 at 7:23 AM Ross Street <ross.street@mq.edu.au> wrote:
Eilenberg and Ulam were both students of Kuratowski I believe, if that is relevant. I remember Sammy talking about him but I can’t remember the topic. Ross
Sent from my iPhone
On 10 Jun 2024, at 9:00 PM, Noam Zeilberger < noam.zeilberger@lix.polytechnique.fr> wrote:
Dear all,
I was wondering if anyone here might be able to provide some additional historical context for a passage in Stanisław Ulam's autobiography "Adventures of a Mathematician", where he talks about his Master's thesis at the Lwów Polytechnic Institute:
I worked for a week on the thesis, then wrote it up in one night, from about ten in the evening until four in the morning, on my father's long sheets of legal paper. I still have the original manuscript. (It is unpublished to this day.) The paper contains general ideas on the operations of products of sets, and some of it outlines what is now called Category Theory.
Without wanting to read too much into his offhand remark, I'm curious about what he was talking about. I noticed that the Wikipedia article on Category theory also alludes to this but does not elaborate or give references. ("Stanislaw Ulam, and some writing on his behalf, have claimed that related ideas were current in the late 1930s in Poland.") According to the information I found online, the Stanislaw M. Ulam Papers are stored in the American Philosophical Society library in Philadelphia, and include copies of both his Master's thesis in Polish titled "O operacje produkto" as well as a 1973 English translation "On the operation of product". But I was not able to find digital copies of these.
Is anyone familiar with the contents of the thesis and can suggest what Ulam was referring to by "outlines" of category theory? Or do you know if Ulam wrote about category theory elsewhere, or if he had any significant interactions with category theorists?
this is just for curiosity, but thanks in advance for any leads! Noam
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