Re: Category without objects

[Uwe Egbert Wolter <Uwe.Wolter@ii.uib.no>]

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

On 2015-03-06 00:45, Peter LeFanu Lumsdaine wrote:
> We actually had a post-seminar reference-hunt on this in Stockholm
> quite recently, and found that the arrows-only definition goes right
> back to Mac Lane 1948, ???Groups, Categories, and Duality???:
> http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1079106/pdf/pnas01707-0037.pdf
>
>
> This cites two earlier papers only along with the definition (Mac Lane
> 1942 and Eilenberg???Mac Lane 1945 ??? the first two papers to mention
> categories, right?), but both of those used the objects-and-arrows
> formulation.  So it seems that the two-sorted formulation was
> considered right from the start, and the arrows-only version either
> from the start or very soon afterwards.
>
> Of course, the original question has already been well answered, but I
> guess the extra history may be of interest to others as well.
>
> Best,
> ???Peter.
>

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