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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 11th 2011
   • (edited Mar 11th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have created an entry [[model structure on dg-modules]] in order to record some references and facts. I think using this I now have one version of the statement at [[schreiber:derived critical locus]] that is fully precise. But I am still trying to see a better way. This is fiddly, because 1. contrary to what one might expect, thre is not much at all in the literature on general properties homotopy limits/colimits in [[dg-geometry]]; 1. and large parts of the standard toolset of homotopy theory of oo-algebras does not apply: * the fact that we are dealing with _commutative_ dg-algebras makes all Schwede-Shipley theory not applicable, * the fact that we are dealing with oo-algebras in chain complexes makes all Berger-Moerdijk theory not apply; * and finally the fact that we are dealing with dg-algebras under another dg-algebra makes Hinich's theory not apply! That doesn't leave many tools to fall back to.

   I have created an entry model structure on dg-modules in order to record some references and facts.

   I think using this I now have one version of the statement at derived critical locus (schreiber) that is fully precise. But I am still trying to see a better way. This is fiddly, because

   1. contrary to what one might expect, thre is not much at all in the literature on general properties homotopy limits/colimits in dg-geometry;

   2. and large parts of the standard toolset of homotopy theory of oo-algebras does not apply:

      • the fact that we are dealing with commutative dg-algebras makes all Schwede-Shipley theory not applicable,

      • the fact that we are dealing with oo-algebras in chain complexes makes all Berger-Moerdijk theory not apply;

      • and finally the fact that we are dealing with dg-algebras under another dg-algebra makes Hinich’s theory not apply!

   That doesn’t leave many tools to fall back to.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeMar 11th 2011
   • PermaLink
   Author: zskoda
   Format: MarkdownItexI do not understand the last statement. Are you talking about undercategories or algebra in categories of modules over dg algebra ?

   I do not understand the last statement. Are you talking about undercategories or algebra in categories of modules over dg algebra ?