Talk:Background and genesis of topos theory

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You have new messages (last change).

Three things:

1. "...barrier to having a good geometric theory (in which it was somewhat like a compact manifold)..."

I don't understand what's between the parentheses.

2. "In the light of later work (c. 1970), 'descent' is part of the theory of comonads;"

I don't like this. 'Descent' is a technique for proving things. It's possible to describe the technique using comonads, but in practice, at least in geometry, it isn't done this way.


3. "The current definition of topos goes back to William Lawvere."

I don't think this is right. Papers in geometry use "topos" to mean "Grothendieck topos." Papers in logic or pure category theory use "topos" to mean "elementary topos." Grothendieck topoi are special cases of elementary topoi but I don't think this makes a difference to geometers.

Anyone disagree strongly?

Changbao 20:32, 19 July 2006 (UTC)

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