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    • CommentRowNumber1.
    • CommentAuthorHurkyl
    • CommentTimeFeb 25th 2021

    I added the description of lax (co)limits of Cat-valued functors via (co)ends and ordinary (co)limits. I should probably flesh this out more.

    I’ve adopted the convention on twisted arrows at twisted arrow category, which is opposite of that in GNN.

    In the case of ordinary 2-category, when the diagram category is a 1-category, is the expression of lax (co)limits via ordinary weighted (co)limits really as simple as taking the weights C /C_{\bullet/} or C /C_{/\bullet}? I can’t find a reference that spells that out clearly; if there really is such a simple description it should be put on the lax (co)limit page.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeFeb 25th 2021

    Corrected an error, so I changed it to something true until I sort out how to agree with the existing convention on nLab.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorHurkyl
    • CommentTimeMar 5th 2021

    Forgot to remove the reference to the twisted arrow category after removing it from the equivalent formulas

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeMar 5th 2021

    Added in the oplax variants. Also corrected an error where I had defined the lax colimit with the oplax formula.

    diff, v8, current

  1. Added the example of the lax limit of an arrow.


    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorHurkyl
    • CommentTimeMar 25th 2021

    Decided it was also worth mentioning the lax colimits over an arrow.

    diff, v11, current

    • CommentRowNumber7.
    • CommentAuthorHurkyl
    • CommentTimeMar 27th 2021

    Clarified the functorality of the slices being used.

    diff, v13, current

    • CommentRowNumber8.
    • CommentAuthorHurkyl
    • CommentTimeOct 20th 2021

    Fixed the variance on the correspondence to the contravariant version. To go along with it, added the (op)lax colimits of a constant functor as an example.

    diff, v14, current

    • CommentRowNumber9.
    • CommentAuthorHurkyl
    • CommentTimeOct 20th 2021

    Ack, I had the variance right the first time, so I’ve reverted that. But I kept the added example and clarification.

    diff, v14, current

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