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nLab > Latest Changes: polynomial functor

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 10th 2014

    added to polynomial functor the evident but previously missing remark why it is called a “polynomial”, here.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 12th 2016

    I added some remarks to polynomial functor: “being polynomial” is a mere property of a (strong) functor once its domain and codomain are identified with slices of an ambient category, cartesian transformations between polynomial functors can be identified on the polynomial data, and the bicategory of polynomial functors enhances to a double category.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 12th 2016

    I made what I thought were similar remarks at the section on polynomial endofunctors at tree, in particular about a double category structure. Could you please have a look, Mike?

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeSep 12th 2016

    Yes, this is all in Gambino-Kock, right? I guess maybe they don’t explicitly write down a version of the double category that contains only cartesian cells.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeSep 12th 2016

    I don’t remember seeing Gambino-Kock; I just took a guess based on what was in Kock’s article referenced in tree.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeSep 12th 2016

    here’s the link; the double category is in section 3.

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeApr 20th 2020

    Added reference

    It would be nice to mention some of the results in this paper in the body too, but I don’t have time.

    diff, v31, current

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