Re: Bourbaki & category theory

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

It seems to me that all this discussion concerning whether the notion of
isomorphism comes before of that of morphism or the other way around, or
if Bourbaki had it or not,  is meaningful only on historical basis.

The notion of category as an abstraction of the notion of morphism would
had been forgotten and it would have disappear from mathematical practice.

What happened, as an unexpected consequence of the definition of
category,  was that the notion of universal property found its home, and
may be this is what Bourbaki, which already had the notion of universal
property, missed (I say may be).

This we can see it from the beginning of the first substantial
contributions of categories to mathematics, as for example in the work
of Kan on adjoint functors, or in the fact that a trivial statement as
Yoneda's Lemma is the most important fact in Category Theory.

e.d.

On 23/05/12 08:36, George Janelidze wrote:
> I am ready to take back my criticism and apologize, if the "longer
> sentence" is correct. But is it?
>
> I am certainly not an expert in Bourbaki history, and, as far as I
> remember, they say no word about morphisms in the historical part of
> "Theory of Sets" and give no references on categories. But I think they
> "always" believed that structures determine isomorphisms but not
> morphisms, and I don't think they changed their mind between 1951 and 1957.
>
> When I say "they" I mean "those of them who made main decisions about
> the Bourbaki tractate". Because I hope (!) that not all of them were
> happy that categories are not even defined in the tractate.
>
> In my previous message I wrote "Removing Bourbaki's formalism..." but in
> fact that "formalism" is (not nice but) serious, in the sense that it
> takes us further away from abstract categories.
>
> Anyway, we need to know, if it is still possible, how exactly did
> Bourbaki definition of morphism(s) came up.
>
> George
>

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