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    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeNov 16th 2018

    The page on inductive-inductive types refers to dialgebras without specifying them. Having a short page as some sort of reference is helpful.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeNov 16th 2018

    The general style of the nLab is to have concepts in the singular, so I’m removing the pluralisation of the page.

    v1, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeNov 16th 2018

    Thanks!

  1. I added references to some relatively recent work on dialgebras advancing the study of their applications to program semantics (in particular using quotient objects instead of final objects).

    Vincenzo Ciancia

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeMay 28th 2020

    Mention that dialgebras were originally introduced by Lambek as “subequalizers”.

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeNov 22nd 2022

    Cross-link with inserter.

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 22nd 2022

    In the recent nnLab discussions on quantum modal logic, wasn’t the need for some construction like a dialgebra, F(x)G(x)F(x) \to G(x), expressed?

    Or was it perhaps to what would be the morphisms in the Kleisli set-up, F(x)G(y)F(x) \to G(y)? Perhaps a ’diKleisli morphism’?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 22nd 2022
    • (edited Nov 22nd 2022)

    I ended up not seeming to have use for it after all, but a couple (literally) of references on the “two-sided Kleisli category” are since being referenced there.

    I haven’t thought about relating this to di-morphisms, but it seems suggestive.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 22nd 2022
    • (edited Nov 22nd 2022)

    Added a reference

    A dialgebraic account of labeled transition systems is in

    • Fabrizio Montesi, Marco Peressotti, Linear Logic, the π\pi-calculus, and their Metatheory: A Recipe for Proofs as Processes (arXiv:2106.11818)

    diff, v6, current

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 22nd 2022

    And also

    • Jim de Groot, Dirk Pattinson, Modal Intuitionistic Logics as Dialgebraic Logics, LICS ’20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science July 2020, 355–369 (doi:10.1145/3373718.3394807).

    diff, v6, current

    • CommentRowNumber11.
    • CommentAuthorDavid_Corfield
    • CommentTimeNov 22nd 2022

    One more

    • Erik Poll, Jan Zwanenburg, From Algebras and Coalgebras to Dialgebras, Electronic Notes in Theoretical Computer Science 44(1), May 2001, 289-307, (doi:10.1016/S1571-0661(04)80915-0).

    diff, v7, current

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