Re: "First" use of 'Category theory' to describe our field

[George Janelidze <george.janelidze@uct.ac.za>]

Dear Colleagues,

I would like to add three remarks to this discussion:

1. In his paper "Samuel Eilenberg and Categories" (Journal of Pure and
Applied Algebra 168 (2002) 127–131), Saunders Mac Lane, talking about [S.
Eilenberg and S. Mac Lane, General theory of natural equivalences,
Transactions of the American Mathematical Society 58, 2 (1945) 231-294]
says:

      "...At the time, Sammy stated firmly that this would be the only paper
needed for category theory. Probably what he had in mind was that the trio
of notions - category, functor, and natural transformation - was enough to
make good applications possible; in particular it was enough to formulate
the axiomatic treatment of homology theory carried out in the famous
Eilenberg--Steenrod text “Foundations of Algebraic Topology”.
      This initial paper on category theory was certainly a “far out”
endeavor; it might not have seen the light of day! Also the terminology was
largely purloined: “category” from Kant, “natural” from vector spaces and
“functor” from Carnap. (It was used in a different sense in Carnap’s
influential book “Logical Syntax of Language”; I had reviewed the English
translation of the book (in the Bulletin, AMS) and had spotted some errors;
since Carnap never acknowledged my finding, I did not mind using his
terminology.)
      Sammy’s initial idea that one paper would be enough turned out to be
wildly wrong. Other basic examples such as adjoint functors were developed;
at Columbia University Sammy subsequently inspired and guided a remarkable
group of young mathematicians who took up category theory: John Gray, Daniel
Kan, Bill Lawvere, Mike Barr, Jon Beck, Alex Heller, Peter Freyd, and many
others. Sammy and I were very fortunate in our students and associates..."

2. We celebrated 50th Anniversary of Category Theory in 1995 twice: in
Halifax (Canada) and then in Cambridge (UK). In particular, the webpage
https://www.mta.ca/~cat-dist/ct95.html says:

"...Fifty years after the paper which founded Category Theory and
twenty-five years after the discovery of Elementary Topos Theory, the
Category Theory community met in Halifax..."

3. Yes, the title "General theory of natural equivalences" has no categories
in it, and one might have different opinions on "which paper has the most
important contribution in transforming 'language' into 'theory'" (what about
[S. Mac Lane, Duality for groups, Bulletin of the American Mathematical
Society 56 (1950) 485-516]?). But I think the citations above clearly
suggest to say that Category Theory was 'officially' born in 1945, and let
us hope to celebrate its 100th Anniversary in 2045!

Of course all this means no disrespect for great contributions of
non-North-American authors mentioned (or not mentioned) in various messages
on this topic.

Best regards,
George


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