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    • 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)



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

    uUR 0U\coprod_{u\in U}\mathbf{R}^0 \to U

    for every cartesian space UU.

    The sheaf condition with respect to JJ yields a smooth set, whereas the separated presheaf condition with respect to KK 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