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nLab > Latest Changes: regular category

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 15th 2021

    added publication details for this reference:

    and am copying it over to compactly generated topological space, too

    diff, v54, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021
    • (edited Apr 16th 2021)

    made more explicit the statement that all those notions of epimorphisms agree in regular categories (here)

    diff, v55, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2021

    added (here) the example GrpGrp which prointer to where in Borceux this is discussed.

    diff, v59, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2021

    The fact that cgHauscgHaus is regular was mentioned in the references, but not in the list of Examples, which ended instead with the counter-example saying that TopTop is not regular.

    So I have added mentioning of cgHauscgHaus also in the list of examples, now here.

    diff, v60, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2021

    added pointer to:

    diff, v61, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 9th 2021
    • (edited Nov 9th 2021)

    I have fixed the (previously somewhat weird) referencing of the original text and added the DOI-link:

    diff, v63, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2021

    I have added (here) compactly generated GG-spaces to the list of examples.

    diff, v64, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2022

    added pointer to

    for the claim that every topos is regular. (Also added pointers to other references for this fact. see here)

    diff, v67, current

    • CommentRowNumber9.
    • CommentAuthormaxsnew
    • CommentTimeSep 15th 2022

    xref with allegories

    diff, v71, current

    • CommentRowNumber10.
    • CommentAuthorʇɐ
    • CommentTimeSep 4th 2023

    I’m not sure what definition 2.5 (A regular category is a finitely complete category with pullback-stable image factorizations.) is supposed to mean; should it be “a finitely complete category for which (regular epis, monos) is a stable factorization system” instead (cf. theorem 1.14 of Gran’s An introduction to regular categories)? (That’s less trivial than “pulling back the image of f yields another mono, and the pullback of f factors through it”.)

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 4th 2023

    I see that this question came up before in MO:q/252815 with essentially the same clarification proposed there in MO:252842.

    Since the originator of the nLab wording didn’t object there, I went ahead and added the clarification (here).

    diff, v75, current

1 to 11 of 11

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