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nLab > Latest Changes: Rel

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  1.  
    • CommentRowNumber1.
    • CommentAuthorJohn Baez
    • CommentTimeSep 3rd 2018

    I added some material about monads and adjunctions in the 2-category Rel and decided to distinguish this 2-category from the 1-category of relations, hoping this will make it a bit easier to state lots of results about both without getting mixed up.

    diff, v23, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeSep 4th 2018

    Good idea, thanks.

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeOct 5th 2022

    Mentioned relations in a category with a suitable factorisation system.

    diff, v28, current

  4. Adding pointer to

    Andre Kornell, Axioms for the category of sets and relations (arXiv:2302.14153)

    Katherine

    diff, v29, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeJan 30th 2024

    Added a reference, “Bicategories of spans and relations”.

    diff, v31, current

    • CommentRowNumber6.
    • CommentAuthormattecapu
    • CommentTimeSep 5th 2024

    clarify that Span->Rel is in fact a pseudofunctor

    diff, v32, current

    • CommentRowNumber7.
    • CommentAuthorElisha Goldman
    • CommentTimeMay 11th 2025
    • (edited May 11th 2025)
    "Rel has very few (co)limits" seems a little bit hyperbolic to me since it's cocomplete (it's the Kleisli category of a monad on a cocomplete category), I feel like this should be edited a little for clarity but idk
    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeMay 11th 2025

    Kleisli categories do not generally have many colimits. They only inherit coproducts from their base, not arbitrary colimits.

1 to 8 of 8

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