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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 10th 2014

    added to polynomial monad the article by Batanin-Berger on homotopy theory of algebras over polynomial monads.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 12th 2016

    I added some discussion of “cartesian polynomial monads” to polynomial monad, and their relationship to clubs and object classifiers. I am currently finding this perspective very helpful; for some reason polynomial functors feel like a much more natural thing to me than clubs, so it is nice that they are almost the same thing.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeApr 3rd 2017

    All the references at polynomial monad define a polynomial monad to be one whose underlying endofunctor is a polynomial functor and whose unit and multiplication are cartesian natural transformations. I am inclined to alter our page polynomial monad to conform to this terminology, unless I hear objections.

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeApr 4th 2017

    If there are interesting examples of non-cartesian polynomial monads, then the terminology on our page is a useful generalization. (But there should still be a note added that most references require all polynomial monads to be cartesian.) If not, then sure, change it.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeApr 4th 2017

    I don’t know of any such examples. But even if there were such examples, for the terminology to be a useful generalization I would argue that there ought also to be interesting theorems about non-cartesian polynomial monads, and I don’t know any of those either.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeApr 7th 2017

    Ok, I made the change.

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