I think that given two augmented dga algebras $A$ and $A'$ and a quasi isomorphism between the respective bar constructions $BA\tilde\to BA'$ there is in general a quasi isomorphism in the other direction $BA'\tilde\to BA$. I cannot find a good source for this however so if someone knows where I can read about it please share!
2026-03-30 14:18:02.1774880282
quasi-isomorphisms between bar/cobar constructions are invertible
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