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nLab > Latest Changes: anafunctor

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 10th 2018

    Added link to my notes on formal anafunctors, here

    diff, v102, current

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 15th 2018

    Added arXiv link to my recent anafunctors notes

    diff, v104, current

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 17th 2018

    Added proper reference to Makkai’s paper as well as link to the published version

    diff, v105, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeMay 23rd 2021

    Improved the remarks about size questions with reference to axioms and countermodels.

    diff, v108, current

  5. fix typo

    julian rohrhuber

    diff, v109, current

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeSep 30th 2022

    Typo fix.

    diff, v110, current

  7. replaced links to the functor comprehension principle (michaelshulman) article on the michaelshulman wiki with links to the functor comprehension principle article on the nlab wiki

    C. Silva

    diff, v111, current

  8. Also removing old discussion in query box:

    Urs says: Why do you restrict this to the abelian case? From page 16 of Noohi’s article I got the impression that he is precisely describing the ana-2-functors between one-object 2-groupoids in terms of the corresponding (possibly nonabelian) crossed modules.

    Mathieu says: I don’t see that (or something like that) on that page, but saturated anafunctors should correspond to butterflies also in the semi-abelian case (using the notion of internal crossed module in a semi-abelian category introduced by Janelidze), but I have not checked it. The special case of groups is probably easy to check: saturated anafunctors between two internal groupoids in the category of groups should correspond to butterflies between the corresponding crossed modules.

    Urs says: I haven’t checked the details. But he is looking at derived homs of crossed complexes. By general nonsense these derived hom should be given by homs out of cofibrant replacements. This is another way of talking about the anafunctor picture. Somebody should check the details.

    Tim: Noohi has pointed out to me a slip in his HHA article in which he gives an ’algebraic’ description of weak map (and thus of anafunctor) between the crossed modules corresponding to the 2-groups. He has posted a corrected version on the archive (<http://arxiv.org/abs/math/0506313v3>, but make sure you get version 3).

    C. Silva

    diff, v111, current

1 to 8 of 8

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