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nLab > Latest Changes: separated presheaf

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 15th 2010
    • (edited Dec 15th 2010)

    I worked a little on the entry separated presheaf. Apart from some general editing I

    • added construction and proof of the separafication functor;

    • began a section on the full notion of bi-separated presheaf.

    More deserves to be done here, but I have to stop for the moment.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeDec 15th 2010

    It would be good to move biseparated to a separate entry. It is a much more rarely used concept.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 20th 2013

    Added the remark that a constant sheaf on a site for which every covering family is inhabited is in fact separated (as per my recent MO question/answer).

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2013

    Thanks! I have cross-lined a bit with locally connected site.

    If you find a minute, please consider either adding a pointer to the proof or the proof itself (simple as it may be, but for completeness).

    • CommentRowNumber5.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 18th 2022
    • (edited Dec 15th 2022 by Urs)

    Added:

    Examples

    Diffeological spaces are biseparated presheaves for the bisite structure on cartesian spaces, where J is the usual topology of open covers and K is the topology given by the families

    ∐u∈UR0→U

    for every cartesian space U.

    The sheaf condition with respect to J yields a smooth set, whereas the separated presheaf condition with respect to K makes it into a diffeological space.

    diff, v18, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 19th 2022

    I have added (here) an Examples-environment and fixed the broken link to diffeological spaces.

    diff, v19, current

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeDec 14th 2022

    Added a reference to epipresheaf.

    diff, v21, current

1 to 7 of 7

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