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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2009
   • PermaLink
   Author: Urs
   Format: Markdownexpanded the Idea-section at <a href="http://ncatlab.org/schreiber/show/%E2%88%9E-Lie+differentiation+and+integration">schreiber:oo-Lie differentiation and integration</a> and polished the section of oo-Lie diffeentiation somewhat, following the blog discussion <a href="http://golem.ph.utexas.edu/category/2006/09/this_weeks_finds_in_mathematic.html#c030600">here</a>

   expanded the Idea-section at schreiber:oo-Lie differentiation and integration and polished the section of oo-Lie diffeentiation somewhat, following the blog discussion here

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2009
   • PermaLink
   Author: Urs
   Format: Markdownsomewhat complementary to the above, added now also to <a href="http://ncatlab.org/schreiber/show/path+%E2%88%9E-groupoid">schreiber:path oo-groupoid</a> a section <a href="http://ncatlab.org/schreiber/show/path+%E2%88%9E-groupoid#InfPathInclusion">Inclusion of infinitesimal paths</a> that provides the basis for <a href="http://ncatlab.org/schreiber/show/integration+of+%E2%88%9E-Lie+algebroid+valued+differential+forms">integration of oo-Lie algebroid valued differential forms</a>. In the <a href="http://golem.ph.utexas.edu/category/2006/09/this_weeks_finds_in_mathematic.html#c030600">blog comment</a> to John Baez I said I need to assume representables to be contractible for this to work, but now I think it works generally. I might be making a mistake, though...

   somewhat complementary to the above, added now also to schreiber:path oo-groupoid a section Inclusion of infinitesimal paths that provides the basis for integration of oo-Lie algebroid valued differential forms.

   In the blog comment to John Baez I said I need to assume representables to be contractible for this to work, but now I think it works generally. I might be making a mistake, though...

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2009
   • PermaLink
   Author: Urs
   Format: Markdowner, there's a problem with what I wrote. I'll fix it later, gotta run now...

   er, there's a problem with what I wrote. I'll fix it later, gotta run now...

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 30th 2009
   • (edited Jan 20th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownMy claim yesterday of the weak equivalence <latex> \Pi^{inf}(X) \simeq \Pi(X) </latex> was bogus. I removed the corresponding discussion and replaced at <a href="http://ncatlab.org/schreiber/show/integration+of+%E2%88%9E-Lie+algebroid+valued+differential+forms">schreiber:integration of oo-Lie algebroid valued forms</a> the affecteed discussion with a (hopefully) correct new discussion following the blog discussion I also expanded the Idea-section at <a href="http://ncatlab.org/schreiber/show/%E2%88%9E-Lie+algebroid">schreiber:oo-Lie algebroid</a> I also improved the definition there. Now the definition uses notions entirely internal to oo-Lie groupoids. The previous definition in terms of Chevalley-Eilenberg algebras is now a consequence of the new definition.

   My claim yesterday of the weak equivalence was bogus.

   I removed the corresponding discussion and replaced at schreiber:integration of oo-Lie algebroid valued forms the affecteed discussion with a (hopefully) correct new discussion

   following the blog discussion I also expanded the Idea-section at schreiber:oo-Lie algebroid

   I also improved the definition there. Now the definition uses notions entirely internal to oo-Lie groupoids. The previous definition in terms of Chevalley-Eilenberg algebras is now a consequence of the new definition.