Re: The humility topos

[Colin McLarty <colin.mclarty@case.edu>]

Yes, this is Grothendieck's stated intention, in the article "Topos"
written with Verdier in SGA 4 (p. 301).

But at the same time he and his friends knew well that topo, with
plural topos, is ordinary French for a little speech, and is common
slang for a school essay.  This comes from the long-time use of
"topos" as a term in rhetoric taken from Aristotle.

I have not found older uses of the specific term "humility topos," but
"topos" in this rhetorical sense is not postmodern.  It is one of the
oldest scholarly terms.

Colin



2010/7/2 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.

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