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nLab > Latest Changes: conservative cocompletion

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  1.  
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeApr 14th 2023

    Create a stub.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeApr 22nd 2024

    Added reference to Makkai–Paré.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeApr 24th 2024

    Why does one need to take the closure under small colimits? Isn’t [Cop,Set]Φ already cocomplete, because it’s reflective in [Cop,Set]? I thought this was the point of the Freyd-Kelly paper Categories of continuous functors.

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeApr 25th 2024

    Modified the explicit description of the conservative cocompletion, which was unnecessarily convoluted.

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeApr 25th 2024

    Mention a consequence of the existence of the conservative cocompletion.

    diff, v7, current

    • CommentRowNumber6.
    • CommentAuthorʇɐ
    • CommentTimeApr 25th 2024

    Restored a co- (haplololologized by revision 5), for nsistency.

    diff, v8, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeJan 6th 2025

    Added some examples and references.

    diff, v9, current

    • CommentRowNumber8.
    • CommentAuthorSam Staton
    • CommentTime5 days ago

    Discussed symmetric monoidal and cartesian closed structure.

    diff, v12, current

    • CommentRowNumber9.
    • CommentAuthorSam Staton
    • CommentTime5 days ago
    • (edited 5 days ago)

    Hi I am not sure whether this page, and the title “conservative cocompletion”, is supposed to be about colimit completion preserving Φ colimits for a given class Φ, or about colimit completion preserving all existing colimits (i.e. only in the case when Φ is precisely the class of colimits that exist). If the latter, I think we should have a page for the former, and my edits should probably have gone there. But I can’t find one, and I’m not aware of a nice name for this, is there one (could say “models” in the sense of sketches, but that’s quite a generic and overused word)? Or does “Φ-conservative cocompletion” already mean the former?

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTime5 days ago

    Probably best for the time being to create subsections for the different cases in this one entry.

    If and when these subsections individually grow large then it will still be easy to split them into distinct entries.

    • CommentRowNumber11.
    • CommentAuthorvarkor
    • CommentTime5 days ago
    • (edited 5 days ago)

    One can talk about the Φ-conservative Ψ-cocompletion. At the moment, the page currently only describes the case in which Ψ is the class of small colimits, but it would make sense also to mention the more general situation.

    • CommentRowNumber12.
    • CommentAuthorSam Staton
    • CommentTime4 days ago

    Note algebras for Lawvere theories as examples

    diff, v13, current

    • CommentRowNumber13.
    • CommentAuthorSam Staton
    • CommentTime4 days ago

    Trying to clear up the different terminologies, as discussed at nforum.

    diff, v13, current

    • CommentRowNumber14.
    • CommentAuthorSam Staton
    • CommentTime4 days ago

    Extensive sheaves example.

    diff, v13, current

1 to 14 of 14

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