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The theory of symmetric operads in chain complexes (say over a good enough field) is in some sense nice, because we have a well defined homotopy theory.

In particular we have a notion of infinity-morphisms of operads (maybe called homotopy morphisms instead), which can be defined as a cooperad map between the appropriate bar constructions of the operads. This is useful as it gives an explicit way to compute inverses to quasi-isomorphisms, by what is sometimes called the "moves of Martin Markl".

Now my question is: Is there a way to explicitly invert a quasi-isomorphism of symmetric co-operads in chain complexes (say over a nice enough field), too?

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