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nLab: Segal conditions and coverages

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    • CommentRowNumber1.
    • CommentAuthorSB
    • CommentTimeJun 29th 2020
    It seems that there is a mistake in the definition of coverages in https://ncatlab.org/nlab/show/Segal+condition#InTermsOfSheafConditionForSimplicialObjects:
    the coverage over the point \Delta[0] is empty, and for any sheaf its fiber over \Delta[0] is a singleton.
    Should any coverage instead be the union of all the maps from the interval \Delta[1] and all the maps from the point \Delta[0]?
    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJun 30th 2020

    Presumably, the definition should say n>0.

    • CommentRowNumber3.
    • CommentAuthorSB
    • CommentTimeJul 1st 2020
    .. and { the identity map of the point } for n=0.

    Anyway, thanks!
    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 2nd 2020

    @SB: No, identity maps are automatically added after saturation, it is not necessary to include them.

1 to 4 of 4

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