Re: Category without objects

[Peter LeFanu Lumsdaine <p.l.lumsdaine@gmail.com>]

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.

On Fri, Mar 6, 2015 at 1:49 AM, Jiri Adamek <adamek@iti.cs.tu-bs.de> wrote:

> See Definition 3.8 in Herrlich & Strecker: Category
> Theory (42 years old...).
>
> Cheers
> Jiri
>
> xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> xxxxxxxxxxxxxxx
> alternative e-mail address (in case reply key does not work):
> J.Adamek@tu-bs.de
> xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> xxxxxxxxxxxxxxx
>
>
> On Thu, 5 Mar 2015, Uwe Egbert Wolter wrote:
>
>  Some years ago (around 30?) I read a book where it was mentioned that
>> one could define categories without (explicit) objects in the sense that
>> objects are mimicked by identity morphisms. Unfortunately, I can not
>> reconstruct what book it was.
>>
>> I know how this works. I would, however, like to have a reference.
>>
>> Best
>>
>> Uwe Wolter
>>

[For admin and other information see: http://www.mta.ca/~cat-dist/ ]