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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJun 17th 2016

    Expanded dinatural transformation a little with examples and references.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 17th 2016

    I’m very glad you did, because it was through the Paré and Román reference that I relocated examples of dinatural transformations (due to Freyd) that I thought were forever lost to buried memory. I may copy them out later.

    • CommentRowNumber3.
    • CommentAuthorRodMcGuire
    • CommentTimeJun 17th 2016

    All I did in my edit was to fix the bad link in:

    Here is a blog post inspired by the above discussion that discusses these concepts in the context of the programming language Haskell:


    Dinatural transformations and coends

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 16th 2020


    • Guy McCusker, Alessio Santamaria, A Calculus of Substitution for Dinatural Transformations, I, (arXiv:2007.07576)

    diff, v21, current

    • CommentRowNumber5.
    • CommentAuthorHurkyl
    • CommentTimeAug 15th 2020

    Added a yoneda-like correspondence between dinatural transformations and natural transformations between certain hom-sets.

    Also, the discussion in “dinaturality vs extranaturality” has some errors. In particular, in the “bending” calculation, G(x,y) F(y,x)G(x,y)^{F(y,x)} doesn’t make sense. Is it supposed to be D(F(y,x),G(x,y))D(F(y,x), G(x,y)) similar to the yoneda-like description I added?

    diff, v22, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeAug 15th 2020

    Yes, I think that’s what’s meant. In fact what’s going on here is basically the same as in your two-sided Yoneda lemma: the hom-profunctor is a representing object for extranatural transformations.

    I don’t see any other errors, what else do you have in mind?

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 24th 2020


    diff, v23, current