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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 2nd 2012
    • (edited Dec 2nd 2012)

    I have started making notes at differential cohesion on the axiomatic formulation of

    So far just the bare basics. To be expanded…

    The basic observation (easy in itself, but fundamental for the concept formation) is that for any differential cohesive homotopy type XX, the inclusion of the formally étale maps into XX into the full slice over XX is not only reflective but also co-reflective (since the formally étale maps are the Pi_inf-closed morphisms with the infinitesimal path groupoid functor / de Rham space functor Π inf\Pi_{inf} being a left adjoint).

    This means that for GG any differential cohesive \infty-group with the corresponding de Rham coefficient object dRBG\flat_{dR}\mathbf{B}G (the universal moduli for flat 𝔤\mathfrak{g}-valued differential forms), the sheaf of flat 𝔤\mathfrak{g}-valued forms over any XX is given by the sections of the coreflection of the product projection X× dRBGXX \times \flat_{dR}\mathbf{B}G \to X into the formally étale morphisms into XX.

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