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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeMar 5th 2012

    The sheafification of a (1-)presheaf on a site is classically constructed in a two-step process X ++X^{++}, where X +X^+ consists of matching families in XX, is always separated, and is a sheaf if XX is separated. But the sheafification can also be constructed in a single step by looking at matching families over hypercovers. However, the only published reference I can find which mentions this latter fact is Higher Topos Theory (section 6.5.3), and it doesn’t really give a proof. Does anyone know of a reference on “good old” 1-sheaves which discusses sheafification via hypercovers?