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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 22nd 2010

created rationalization even though it overlaps with the material at rational topological space

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 22nd 2010
• (edited Apr 22nd 2010)

added in a new section Properties a proof (or what I think is a proof) that rationalization preserves homotopy pullbacks of objects of finite type.

What I type there is supposed to be a more or less immediate re-packaging of a technical result due to Halperin-Thomas, which appears in Hess’s review in a polished form somewhat more to the point than Halperin-Thomas’s discussion. My reformulation is supposed to make it even more to the point.

But check.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeApr 22nd 2010
• (edited Apr 22nd 2010)

added comments and links to rationalization on how Toen’s theory of rational homotopy theory in an (infinity,1)-topos provides another way to regard rationalization is a localization of $\infty Grpd$/$Top$.

Wanted to further expand on this, but am running out of time now…

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeAug 23rd 2020

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeAug 23rd 2020

added statement of rationalization via PL de Rham theory, by the fundamental theorem of dg-algebraic rational homotopy theory

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeAug 23rd 2020

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 26th 2021

(Incidentally, the abstract says this is “part of an upcoming book”, without further details. Might it be for Stable categories and structured ring spectra?)

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeJul 26th 2021
• (edited Jul 26th 2021)

thanks to Charles for confirming (here) so I have expanded this out to: