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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2018

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthormattecapu
    • CommentTimeAug 19th 2023

    I reclaimed this page as a disambiguation for horizontal/vertical and tight/loose terminology. Before that was just a redundant explanation of what a double category is, actually clashing with the main entry.

    I thought Ehresmann introduced the horizontal/vertical terminology, but he didn’t. It’d be nice to track down who did to complete the picture.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthormattecapu
    • CommentTimeAug 22nd 2023

    Added reference to Cruttwell-Shulman

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthormattecapu
    • CommentTimeAug 22nd 2023

    Added Leinster’s book as an example of horizontal=loose and vertical=tight convention

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeAug 22nd 2023

    Ordered table chronologically. An early reference for the horizontal/vertical terminology is Dawson and Paré’s papers “Characterizing Tile Orders” and “General associativity and general composition for double categories”.

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthormattecapu
    • CommentTimeOct 25th 2023

    redirects: tight and loose

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthormattecapu
    • CommentTimeNov 15th 2023

    added disambiguation to the header

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeNov 15th 2023

    I’m not sure the disambiguation is necessary: instead we can simply observe on the page that the terms “tight” and “loose” for F-categories are special cases of those for double categories (viewing an F-category as a strict double category with strict companions).