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created rationalization even though it overlaps with the material at rational topological space
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.
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…
added pointer to
added statement of rationalization via PL de Rham theory, by the fundamental theorem of dg-algebraic rational homotopy theory
added pointer to:
added pointer to
(Incidentally, the abstract says this is “part of an upcoming book”, without further details. Might it be for Stable categories and structured ring spectra?)
thanks to Charles for confirming (here) so I have expanded this out to:
I have expanded a little at Rationalization of a homotopy type, adding the Bousfield-Kan formula for rationalization via degreewise Malcev completion of the simplicial loop group, both in the simply/connected/absolute case as well as in the general/relative case.
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