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nLab > Latest Changes: Lack's coherence observation

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  1.  
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeMay 9th 2022

    Could we find a word other than “theorem” to use for this observation? Also, does anyone know where this observation arose initially?

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 9th 2022

    I have touched the sentence here trying to indicate what the issue is with the observation not being a theorem.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeMay 9th 2022

    I think it would also be closer to the truth to call it a conjecture than a theorem, unless there are actually no examples of “naturally occurring” bicategories that are not known to be biequivalent to “naturally occurring” 2-categories. However, “conjecture” suffers from the same issues in “naturally occurring” not being well-defined.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 9th 2022

    I think “observation” would work well.

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeMay 9th 2022

    I think “observation” would work well.

    I like observation much better than theorem :)

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 10th 2022

    Just to say that it looks like you are expert on the subject matter and care about it, in which case you should go ahead and make edits to the entry as you see fit. It is certainly in need of improvement.

    What the entry needs most is any indication that it’s subject matter exists at all, namely references that attribute to Steve Lack whatever it is the entry wants to claim is being attributed to Steve Lack. (Asking Google for this gives essentially just the nLab entry back, which is worrying.)

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeMay 10th 2022

    Rename to “Lack’s coherence observation”. Although it doesn’t have the same ring to it as “Lack’s coherence theorem”, it is more accurate.

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeMay 10th 2022

    Give an abstract justification for the first example.

    diff, v5, current

    • CommentRowNumber9.
    • CommentAuthorvarkor
    • CommentTimeMay 10th 2022

    It may be the case that the example of polynomial functors may also be characterised as a Kleisli–Eilenberg–Moore type situation, because the bicategory of polynomial functors can be seen as a Kleisli category for a relative pseudomonad, as briefly discussed in this talk by Garner.

    • CommentRowNumber10.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 10th 2022

    Filled out bibliography entry for Lack’s paper

    diff, v6, current

1 to 10 of 10

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