Talk:Background and genesis of topos theory

From Wikipedia, the free encyclopedia

Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Start Class	Low Priority	Field: Foundations, logic, and set theory (historical)
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. References are absolutely essential, as this is a history article.--Cronholm144 07:55, 24 May 2007 (UTC)

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)

No (I don't disagree), What this article needs is some reference material.--Cronholm¹⁴⁴ 08:24, 16 July 2007 (UTC)