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nLab > Latest Changes: slice 2-category

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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeNov 3rd 2010

    Created slice 2-category.

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeJan 11th 2021

    I’ve swapped the direction of the natural transformation component of the 1-cells, so that removing the isomorphism condition gives the lax slice 2-category agreeing with the convention in 2-Dimensional Categories by Johnson, Yau.

    Additionally, I’ve explicitly stated the direction of that component in the lax slice 2-category.

    I’m not sure if this is standardized; feel free to revert if nLab has an active preference for the other convention.

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJan 11th 2021

    I don’t know if there is a standard convention, but the one you adopted has the virtue of making the canonical “comma square” of the “lax-slice” a lax natural transformation, so it seems at least reasonable. I added a remark to this effect, and a citation to Johnson-Yau.

    diff, v6, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJan 11th 2021

    (Apparently \sslash is not recognized inside tikzcd?)

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