I remember Henry Whitehead said that he was very impressed by the axioms for a category in the Eilenberg-Mac Lane paper. A curiosity about the definition is that groupoids were defined by Brandy in 1926, and this definition was used by the Chicago school of algebra and applied to ring theory. Bill Cockcroft told me that the groupoid notion was an influence. In 1985 I asked Eilenberg about this, and said no, since if it had been, they would have used it as an example! I forgot to ask Mac Lane! Ronnie Brown On 06/03/2015 14:42, Uwe Egbert Wolter wrote:
Many thanks for all the immediate replies and all the interesting information.
Finally, I could also reconstruct today where I have seen the arrows-only definition around 30 years ago. There is a four page introduction into categories in the first chapter of P.M. Cohn's "Universal Algebra". He outlines that one could do so and gives a corresponding exercise.
Best
Uwe
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