Re: Category without objects

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

It seems to me:

Eheresmann arrived to the concept of categories as a generalization of
groupoids, and he was dealing with small internal categories (the set of
arrows (or elements) were differential manifolds etc). This explains why
he dismissed objects in his later treatment of abstract categories.

Eilemberg and MacLane arrived to the concept of categories as an
abstraction of the large concrete categories of sets with structure and
functions which were considered to be morphisms for the structure.
Objects were essential in this approach.

That the insight of E. M. to do not dismiss objects in the abstract
setting was  wonderful is that to-day we can not conceive groupoids
without objects.


On 7/3/15 11:36, Ronnie Brown wrote:
> 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
>

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