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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2010

    stub for Lie operad

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2010

    I do not understand what do you mean by linear operad ? Lie operad is a quadratic operad in the sense that the relations. It is a Koszul dual quadratic operad to the commutative operad. If you mean by linear to be an operad internal to vector spaces, then please say it internal to vector spaces. But then this is not in accordance to the statement in the entry that the cofibrant resolution is L-infinity operad: the latter is a dg-operad hence, Lie operad is, at least in that statement, consider a dg-operad.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2010
    • (edited Jul 26th 2010)

    By linear operad I mean enriched in vector spaces. As in “linear category”.

    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2010

    OK you call it enriched, operads are usually said in (operad in Top = topological operad). I am happy with that. But this is as I pointed above not in accordance to the main statement you quote that its cofibrant resolution is the L-infinity operad. This is true in the model category of dg-operads, not the operads (enriched) in Vec.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2010
    • (edited Jul 26th 2010)

    But operads in VectVect sit inside the category of operads in chain complexes, where the resolution takes place.

    Just as an operad in sets is resolved after regarding it under the canonical embedding as an operad in topological spaces.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2010
    • (edited Jul 26th 2010)

    Forgetting to say the embedding means being sloppy about the true identity. If you identify a Set operad with extending it Top-operad to be able to resolve it, than in truth you are considering it as a Top-operad to start with. It can be embedded in many other setups with different resolutions. In nlab we should be free from various local jargons and assuming microlocal conventions.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2010

    sure, go ahead and add the details. This is not the only issue that the stub entry didn’t go into…

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2010

    check

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