Re: Bourbaki and Categories

[Michael Barr <barr@math.mcgill.ca>]

I don't know about this.  I took several courses in the late 1950s that
seem to have been influenced by the structuralist ideas (certainly
categories weren't mentioned; I never heard the word until Dave Harrison
arrived in 1959) and each of them started by defining an appropriate
notion of "admissible map".  I do not recall any special point being made
of isomorphism and I think in general it was used for what we now call a
bimorphism (1-1 and onto) even in cases, such as topological groups, when
they were not isomorphisms.

To be sure Bourbaki was not mentioned either, but this structuralist
influence seemed strong.

Michael

On Mon, 15 Sep 2008, Andre.Rodin@ens.fr wrote:

>
> zoran skoda wrote:
>
>
>> The remark that as a proponent of "structures"
>> Bourbaki had to include categories is anyway a bit lacking an argument.
>
>
>
> I think that as a 'proponent of "structures"' Bourbaki had NOT include
> categories - and not only because of the size problem. A more fundamental
> reason seems me to be this. Structures are things determined up to isomorphism;
> in the structuralist mathematics the notion of isomorphism is basic and the
> notion of general morphism is derived (as in Bourbaki).  In CT this is the
> other way round: the notion of general morphism is basic while isos are defined
> through a specific property (of reversibility).
> This is why the inclusion of CT would require a revision of fundamentals of
> Bourbaki's structuralist thinking. Although CT for obvious historical reasons
> is closely related to structuralist mathematics it is not, in my understanding,
> a part of structuralist mathematics - at least not if one takes CT *seriously*,
> i.e. as foundations.
>
> best,
> andrei
>
>
>