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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 $C_{\bullet/}$ or $C_{/\bullet}$? 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.

• 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.

• CommentRowNumber3.
• CommentAuthorHurkyl
• CommentTimeMar 5th 2021

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

• 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.

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

Anonymous

• CommentRowNumber6.
• CommentAuthorHurkyl
• CommentTimeMar 25th 2021

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

• CommentRowNumber7.
• CommentAuthorHurkyl
• CommentTimeMar 27th 2021

Clarified the functorality of the slices being used.

• 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.

• 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.