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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