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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2010

    in preparation of the next session of our Seminar on derived differential geometry I am starting

    infinity-algebra over an (infinity,1)-operad

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeNov 8th 2010

    Is there a reason to put ∞- in front of “algebra” here and at other similar places? Is there any other sort of algebra over an (∞,1)-operad? We don’t talk about “2-algebras” for 2-monads.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2010

    Hm, you think i should change it? It’s somewhat redundant, true, but not entirely without purpose. There is a sensible notion of nn-algebra over a kk-operad/monad for independent n,kn,k.

    But I am not dogmatic about this. Just feeling a bit lazy now to change it all :-)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeNov 8th 2010

    There is a sensible notion of nn-algebra over a kk-operad/monad for independent n,kn,k.

    Such that a 2-algebra over the 1-operad for monoids is a monoidal category, for instance? I guess. That doesn’t seem like a really important reason to keep the prefix for everything else; maybe we could just say that the prefix isn’t really necessary here, but could be used to disambiguate elsewhere.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2010

    Such that a 2-algebra over the 1-operad for monoids is a monoidal category, for instance?

    For instance. Maybe more importantly, such that \infty-algebras over the 1-operads AssAss, CommComm are A A_\infty-algebras, E E_\infty-algebras, etc.

    But, as I said, I can live well with dropping that prefix. I will eventually do so.