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Suppose we are given a fixed ambient symmetric monoidal model category (I'm mostly interested in chain complexes over char zero fields). Then we have the notion of an $E_n$-operad in that category. Moreover we have a model structure for operads, we can speak about homotopy operads, infinity morphism of operads ect.

In such a setting. Is there any interesting structure on the set of all possible (homotopy) $E_n$-operads?

I know, this question is far from being precise. That's basically because I don't know what I'm after at this point. Therefore anything might be interesting.

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  • $\begingroup$ I mean the least thing, I can see is the structure of a groupoid if we work over a field of characteristik zero. In that case all these operads are isomorphic (id we consider infinity morphisms of homotopy operads), since they are all formal. $\endgroup$
    – Mark.Neuhaus
    Commented Sep 21, 2017 at 6:41

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