categories: Re: categorical incunabula

["Hans-E. Porst" <porst@math.uni-bremen.de>]

Concerning Peter Freyd's question

> Saunders's 1948 paper (without Sammy) first surprised me 40 years ago.
> Buchsbaum in his 1955 paper that introduced abelian categories (under
> the name "exact categories") said that he saw no way of defining
> infinite products. Which meant that he hadn't seen Saunders's 1948
> paper. Is this the first appearance of universal mapping definitions?

one certainly might consider A.A. Markov's definition of a free topological
group (in 1945) as an earlier appearance:

A. A. Markov: On free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 9
(1945), 3-64 [Amer. Math. Soc. Transl. 30 (1950), 11-88; Reprint: Amer.
Math. Soc. Transl. Ser. I, 8 (1962), 195-272.]

Note, in this context, also the early apperances of what we now would call
"applications (or predecessors) of Freyd's GAFT" (though none of these
papers has the notions of category or functor)

S. Kakutani: Free topological groups and finite discrete product groups,
Proc. Imp. Acad. Tokyo 20 (1944), 595-598

P. Samuel: On universal mappings and free topological groups, Bull. Amer.
Math. Soc. 54 (1948), 591-598

In his 1957 paper

A. I. Malcev: Free topological algebras, Izv. Akad. Nauk SSSR Ser. Mat. 21
(1957), 171-198 [Amer. Math. Soc. Transl. Ser. II, 17 (1961), 173-200.]

Malcev already begins his proof of the existence of a free topological
algebra (as a topological subgroup of the corresponding product) with the
phrase "In the usual way one can now prove".

-- 
Hans-E. Porst                                 porst@math.uni-bremen.de
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