Re: The humility topos

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

2010/7/6 Graham White <graham@eecs.qmul.ac.uk>:

Raises a very on-point question about Grothendieck's choice of the word "topos":

> One of the most interesting things about the term, at any rate in Greek,
> is that it thus has both logical and geometrical meanings, and that from
> very early. I can't help wondering whether Grothendieck had that in
> mind: he seems to have read widely enough for that to occur to him.

It is not likely that Grothendieck was thinking much of Aristotle.  He
probably was thinking of the common French phrase "tu vois le topo."
In crude translation "you see the topos."  It actually means "you see
the point" or " you know what I am talking about."

Grothendieck's goal for topos theory was to explicate, and
systematize, and vastly generalize a lot of routine arguments, that
had become "commonplaces" in many different uses of cohomology -- so
that as soon as you "see the topos" you know the outline of the
situation.  Then you only need to occupy yourself with a few relevant
particulars to solve a particular problem.

best, Colin



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