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nLab > Latest Changes: concrete sheaf

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 3rd 2010

    expanded concrete sheaf: added the precise definition and some important properties.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2011

    I have added to concrete sheaf a subsection Slice topos over a concrete object with some observations.

    Not sure how useful this is.

    • CommentRowNumber3.
    • CommentAuthorSam Staton
    • CommentTimeAug 5th 2019

    mention well-pointedness and concrete categories. Hope I got this right.

    diff, v23, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeAug 5th 2019

    Removed the link to well-pointedness; I think the latter term is usually only used for toposes.

    diff, v24, current

    • CommentRowNumber5.
    • CommentAuthorSam Staton
    • CommentTimeAug 6th 2019
    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeAug 6th 2019

    Okay; but in that case the link shouldn’t go to well-pointed topos.

    • CommentRowNumber7.
    • CommentAuthorSam Staton
    • CommentTimeAug 8th 2019
    • (edited Aug 8th 2019)
    I see. But the well-pointed topos page already mentions some generalizations (pretoposes, coherent categories). I thought there might be an external/internal theorem for concrete quasitoposes generalizing the theorem for well-pointed toposes. Although I can't find a reference so maybe there isn't in general?
    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeAug 8th 2019

    True, but an arbitrary ccc seems to me like a much further step than a pretopos. And the page points out that the “correct” definition differs depending on what kind of category we’re talking about. In particular, it suggests that for a finite-limit category we should ask that 11 be a strong generator, not just a generator as it is for a concrete category.

    I haven’t thought about well-pointed quasitoposes at all.

  9. Added references on “extensional presheaves”, which are concrete presheaves on trivial sites (what is the best name for a site where only identities are covering?)

    Jonas Frey

    diff, v28, current

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 26th 2023

    Redirects: concretization, concretification.

    diff, v31, current

    • CommentRowNumber11.
    • CommentAuthorSam Staton
    • CommentTimeSep 24th 2024

    Explicit description of concrete presheaf.

    diff, v32, current

1 to 11 of 11

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