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nLab > Latest Changes: monoidal double category

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  1.  
    • CommentRowNumber1.
    • CommentAuthormattecapu
    • CommentTimeAug 18th 2023

    Created page

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeAug 18th 2023

    This is the first time I see the terminology “tight and loose morphisms”. Is this standard?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 18th 2023

    added cross-link with monoidal 2-category

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeAug 18th 2023
    • (edited Aug 18th 2023)

    Re. #2: the terminology was introduced in Lack and Shulman’s Enhanced 2-categories and limits for lax morphisms (in the context of F-categories, which are a special kind of double category), and has become increasingly popular in the context of double categories, since it sidesteps the ambiguity between “horizontal” and “vertical” morphisms (which are used inconsistently in the literature). I’m not sure it could yet be called “standard”, but it is also not uncommon. (Personally, I think it’s a helpful trend.)

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeAug 18th 2023

    The reference is called “Shulman’21”, but the cited paper is from 2010. Was that intended?

    • CommentRowNumber6.
    • CommentAuthorvarkor
    • CommentTimeAug 18th 2023

    Added a reference to Hansen and Shulman.

    diff, v3, current

    • CommentRowNumber7.
    • CommentAuthormattecapu
    • CommentTimeAug 19th 2023
    No Nathaniel, that was a (weird?) typo of mine. Corrected now.

1 to 7 of 7

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