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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeFeb 22nd 2010
   • PermaLink
   Author: Urs
   Format: Markdownstarted [[formal dg-algebra]]

   started formal dg-algebra

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 22nd 2010
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   Author: Urs
   Format: Markdownexpanded a bit more In the old Sullivan reference the condition for A to be formal is that there is a quasi-iso <latex> A \to H^\bullet(A) </latex>. In newer references, such as the survey by Kathry Hess, it says instead that there is a span of quasi-isos between <latex>A</latex> and <latex> H^\bullet(A) </latex>. Since in the model structure on dg-algebras all objects are fibrant, I take it that this is equivalent to saying that <latex> A </latex> and <latex> H^\bullet(A)</latex> are isomorphic in the homotopy category. This is the way I state the definition now. But check if I am mixed up.

   expanded a bit more

   In the old Sullivan reference the condition for A to be formal is that there is a quasi-iso .

   In newer references, such as the survey by Kathry Hess, it says instead that there is a span of quasi-isos between and . Since in the model structure on dg-algebras all objects are fibrant, I take it that this is equivalent to saying that and are isomorphic in the homotopy category. This is the way I state the definition now. But check if I am mixed up.