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nLab > Latest Changes: lax monoidal category

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1 to 19 of 19

  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeMay 31st 2018

    Created, with so far just an overview of all the possibilities.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 31st 2018

    It would be nice to add a link to monoidal category which is currently still spam-locked…

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeMay 31st 2018

    List some related notions and special cases.

    v1, current

    • CommentRowNumber4.
    • CommentAuthorRichard Williamson
    • CommentTimeJul 16th 2018
    • (edited Jul 16th 2018)

    I have now removed the lock on editing the page monoidal category. The commit can be seen on github. I made a trivial edit and then another one to put the page back as it was before, to test that editing was now possible.

    • CommentRowNumber5.
    • CommentAuthorJohn Baez
    • CommentTimeDec 20th 2020

    Added reference to Bourke-Lack paper “Skew monoidal categories and skew multicategories”.

    diff, v2, current

    • CommentRowNumber6.
    • CommentAuthormaxsnew
    • CommentTimeDec 21st 2020

    On the part about oplax monoidal categories, what does “weakly representable” mean? Does it mean satisfying the existence but not uniqueness part of representability (in type theory terminology β\beta but not η\eta)? Is there an appropriate link?

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeJan 6th 2021

    It means the morphism only satisfies a universal property (with an ordinary isomorphism) for multimorphisms without extra objects added on each side. See for instance section 9 of http://tac.mta.ca/tac/volumes/24/21/24-21abs.html.

    • CommentRowNumber8.
    • CommentAuthormattecapu
    • CommentTimeAug 3rd 2022

    add redirects for skew-monoidal

    diff, v4, current

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeSep 28th 2022

    Add a table explaining the relationship between the various notions of lax/skew monoidal categories.

    diff, v5, current

    • CommentRowNumber10.
    • CommentAuthorvarkor
    • CommentTimeSep 28th 2022

    Clarify remark about the “missing” lax monoidal structures.

    diff, v5, current

    • CommentRowNumber11.
    • CommentAuthorvarkor
    • CommentTimeSep 28th 2022

    Mention skew-bicategories.

    diff, v7, current

    • CommentRowNumber12.
    • CommentAuthorBryceClarke
    • CommentTimeOct 25th 2023

    Added the reference:

    diff, v9, current

    • CommentRowNumber13.
    • CommentAuthorvarkor
    • CommentTimeDec 22nd 2023

    Mentioned the terminology “multitensor”.

    diff, v11, current

    • CommentRowNumber14.
    • CommentAuthorvarkor
    • CommentTimeMar 7th 2024

    Added original reference for skew-monoidal categories.

    diff, v12, current

    • CommentRowNumber15.
    • CommentAuthorvarkor
    • CommentTimeJun 12th 2024

    Added a normalisation result for skew-monoidal categories.

    diff, v13, current

    • CommentRowNumber16.
    • CommentAuthorShamrock
    • CommentTimeJul 9th 2024
    It would be nice if someone could add some examples/use cases/motivation
    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeJul 9th 2024
    • (edited Jul 9th 2024)

    added a parenthetical to indicate that first examples were discussed by Szlachányi 2012

    added pointer to

    where examples are claimed of skew-monoidal model categories whose homotopy categories become monoidal

    also, I have touched the wording and hyperlinking in the Idea-section, to be more to the point

    and added pointer to

    needed for the comments on skew-closure that had been there already

    diff, v14, current

    • CommentRowNumber18.
    • CommentAuthorvarkor
    • CommentTimeJul 29th 2024

    Added some earlier references for skew-monoidal categories.

    diff, v16, current

    • CommentRowNumber19.
    • CommentAuthorvarkor
    • CommentTimeAug 2nd 2024

    Added a reference to Grandis’s “biased d-lax 2-categories”.

    diff, v17, current

1 to 19 of 19

  1.