Re: Bourbaki & category theory

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

On 21/05/12 19:49, Staffan Angere wrote:
> Dear categorists,
>
> and also, hello everyone, since this is my first post here! I'm wondering about the connection of Bourbaki to category theory. The copy of "Theory of Sets" that I have says it's written in 1970. Yet, Dieudonné famously saiid that the theory of functors subsumed Bourbaki's theory of structures... and, also, Bourbaki's theory of structures is very clearly a theory of a type of concrete categories. On the other hand, I've seen claims  that the categorists' use of "morphism" comes from Bourbaki. So who was first? Does anyone here know when Bourbaki's theory of structures was really conceived? I guess this might be self-evident to anyone born during the 1st half of the 20th century, but it has turned out to be really hard to find out for me.
>
> Thanks in advance,
> staffan
>
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The reason why category theory "is what it is" is that

it is the language that allows to define the notion of universal 
property in its right generality.

The notion of universal property first appears in Bourbaki, which 
decided not to use the language of categories to formulate it, on spite 
of the advice of Grothendieck.

e.d


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