Re: The humility topos

[Steve Vickers <s.j.vickers@cs.bham.ac.uk>]

I've assumed (and told people) that "topos" was a back-formation from
"topology" - that Grothendieck's intention was to imply that toposes
were the structures of which topology was truly the study. (The argument
falls into two parts: (a) to carry out topology you need sheaves and not
just opens, and (b) there are suitable categories of sheaves that don't
arise from ordinary spaces.)

Certainly it is my own intention to stress the "generalized topological
space" nature of toposes; but is my assumption about Grothendieck's
intention actually correct?

Steve.

Dusko Pavlovic wrote:
> It might be fair to remember that "Topoi" is the title of 6th book or
> Aristotle's Organon. "On Categories" is the title of the 1st book of
> Organon.
>
> Both concepts were very actively used by scolastic philosophers.
> Maybe we are their heirs of some sort ;)
>
> It would be interesting to know about the motivations of people who
> introduced these terms into mathematics. I think that MacLane said at
> one point that there was a terminological link through Rudolf Carnap,
> thus through neokantians. The notion of categories plays a prominent
> role in Kant's first Critique. But it is even more interesting if the
> term topos was introduced with an intentional reference to
> *dialectics*, which is what that part of Organon is about.
>
> -- dusko


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