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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeMay 10th 2012
    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeMay 13th 2012

    Nice!

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeJun 11th 2021

    Alternative presentation along the lines of abstract clones. Hope I got this right, I’m not sure of a reference.

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 16th 2022

    To add once editing is back: abstract clones for abstract syntax.

    • CommentRowNumber5.
    • CommentAuthorJ-B Vienney
    • CommentTimeJul 28th 2022
    • (edited Jul 28th 2022)

    Is there any reference on cartesian multicategories or is it brand new research?

    I would like to use it to conceptualize formal definitions about polynomials between vector spaces as in the chapter 1: Polynomials of the book Complex Analysis on Infinite Dimensional Spaces (Seán Dineen). These things are purely formal and thus cartesian multicategories are maybe the good place to talk about polynomials categorically.

    I need a place where I can compose a copy map Δ n:EE n\Delta^{n}:E \rightarrow E^{n} with a nn-linear map f:E nFf:E^{n} \rightarrow F and such a composite Δ n;f\Delta^{n};f would be the definition of an homogeneous polynomial of degree nn from EE to FF.

    Maybe such a place would give a cartesian differential category.

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeJul 28th 2022
    • (edited Jul 28th 2022)

    Added references. I’m not sure what the earliest reference is, but for now I’m not able to find a reference earlier than Pisani’s paper.

    diff, v8, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 17th 2024

    Added the original reference.

    diff, v12, current