Re: Category without objects

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

Much older, 69-70 years old !

In the original paper:

S. Eilenberg y S. Mac Lane, General Theory of Natural Equivalences,
Trans. Amer. Math. Soc. 58 (1945), 231?294.

They already considered the notion of category without objects, but
choose to use objects. They wrote:

"It is thus clear that the objects play a secondary role, and could be
entirely omitted from the definition of a category. However, the
manipulation of the applications would be slightly less convenient were
this done. [p?g. 238]

On spite of this, Ehresmann was a fan of categories without objects:

Erhesman adopted and pushed forward the notion of categories without
objects, writing many papers and a book where categories did not have
objects.

C. Ehresmann, Cat?gories topologiques et cat?gories diff?rentiables,
Colloque G?om. Diff. Globale (Bruxelles, 1958), Centre Belgue Rech.
Math., Louvain, 1959, 137?150.

Eduardo Dubuc


On 05/03/15 13:49, Jiri Adamek wrote:
> See Definition 3.8 in Herrlich & Strecker: Category
> Theory (42 years old...).
>
> Cheers
> Jiri
>
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>
> 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


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