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nLab > nLab General Discussions: "Canonical" functor from E_n algebras into Pois_n algebras?

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    • CommentRowNumber1.
    • CommentAuthorJoWing
    • CommentTimeOct 23rd 2016
    In https://ncatlab.org/nlab/show/Kontsevich+formality it is said, that there is a "canonical" functor from $E_n$-algebras into $Pois_n$-algebras. I'm aware that formality of all $E_n$-operads defines an equivalence of categories of $E_n$-algebras and $Pois_n$-algebras. But to me that sounds different than a *canonical* functor. Mostly because these equivalence are not unique but parameterized for $n=2$ for example by Drinfeld associators.

    Does someone here knows what this *canonical* functor looks like? Or is it better to say that there are equivalences between these categories, which are parameterized, not canonical?

    Best Jo.
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2016

    Hm, isn’t that the functor that takes an E nE_n-algebra to its homology?

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeOct 26th 2016

    (By the way, JoWing: below the comment box you can select your format. If you choose Markdown+Itex, then you can type LaTeX as usual and it will render.)

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