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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeFeb 22nd 2010
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeFeb 22nd 2010

expanded a bit more

In the old Sullivan reference the condition for A to be formal is that there is a quasi-iso $A \to H^\bullet(A)$.

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