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nLab > Latest Changes: strong dinatural transformation

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 20th 2023

    stub

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJul 21st 2023

    I noticed the Neumann’s ’Paranatural Category Theory’ article appearing recently along with your ’Internal parametricity, without an interval’. As ways of dealing with parametric polymorphism, any connection?

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeJul 21st 2023

    The term “paranatural transformation” doesn’t appear to be used anywhere except the recent preprint that David mentions. Is there a reason this was chosen this as the name of the page, rather than “strong dinatural transformation”, which is the standard term?

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 21st 2023

    Added:

    Originally introduced (as strong dinatural transformations) in

    • E. Dubuc, R. Street, Dinatural transformations, In Saunders Mac Lane, ed., Reports of the Midwest Category Seminar IV, v. 137 of Lecture Notes in Mathematics, pp. 126–137. Springer-Verlag, Berlin, 1970.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeJul 21st 2023

    Re. #4, I don’t see that strong dinatural transformations are mentioned in that paper. My impression is that they were introduced in Paré–Román’s Dinatural numbers.

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 21st 2023

    Replaced:

    Originally introduced (as strong dinatural transformations) in Definition 2.7 of

    • Philip S. Mulry, Strong Monads, Algebras and Fixed Points, in: Applications of Categories in Computer Science, London Mathematical Society Lecture Note Series 177, 202–216, doi.

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeOct 27th 2023

    Since I received no response to my question regarding why “paranatural transformation” should be chosen over “strong dinatural transformation”, which is the standard terminology, I have renamed the page.

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorSam Staton
    • CommentTimeJul 24th 2024
    • (edited Jul 25th 2024)

    When DD has pullbacks, am I right that this can be regarded as an ordinary naturality condition for relations?

    For any f:c→c′f:c\to c' we can form a relation R F,f⊆F(c,c)×F(c′,c′)R_{F,f}\subseteq F(c,c)\times F(c',c') by pullback [so R F,f=F(c,c)× F(c,c′)F(c′,c′)R_{F,f}=F(c,c) \times_{F(c,c')} F(c',c'), as on the page].

    And then “strong dinaturality of α\alpha” seems to be the same thing as [edit] relation preservation.

    I would add it to the page but since I haven’t thought about strong dinaturality much before I thought to first check whether this is obviously wrong! [edit: I’ve added it]

    • CommentRowNumber9.
    • CommentAuthorSam Staton
    • CommentTimeJul 25th 2024

    missing link -> archive.org

    diff, v7, current

    • CommentRowNumber10.
    • CommentAuthorSam Staton
    • CommentTimeJul 25th 2024

    Attempt to summarize my understanding of the connection with relational models.

    diff, v7, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJul 25th 2024

    I have uploaded the slides for Vene 2006 to the nLab server,

    and made various minor adjustments to the page’s code, such as hyperlinking the author Varmo Vene, adding doi-s, etc.

    diff, v8, current

1 to 11 of 11

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