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nLab > Latest Changes: double bicategory

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    • CommentRowNumber1.
    • CommentAuthorJohn Baez
    • CommentTimeDec 4th 2009
    I started a little page called double bicategory.
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 4th 2009

    I've felt for a while that what we call "double categories" might better be called "double 2-categories," since they are a lot more like "enhanced" 2-categories than they are like 1-categories. If we called them that, then "double bicategory" for Verity's notion would make perfect sense. Unfortunately "double category" is too entrenched to be changed by now.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeDec 4th 2009

    But can we call them ‘double 2-categories’ in addition to their more prosaic and more common name? Or is that already established for internal 2-categories in some category of 2-categories?

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeDec 4th 2009

    I've never seen it used that way, but I think given the prevalence of "double category" for its current meaning, saying "double 2-category" for the same thing would just create additional confusion, and probably make some people think of internal 2-categories in 2cat whether or not it's been used that way before.

    • CommentRowNumber5.
    • CommentAuthorJohn Baez
    • CommentTimeDec 7th 2009
    I like "double category" since 1) it's already used, 2) it instantly sounds like a relative of "2-categories" and "bicategories", and 3) double categories are categories in Cat.
    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeSep 27th 2021

    Tidying.

    diff, v7, current

1 to 6 of 6

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