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Is it always possible to write a derived manifold as a homotopy colimit of principal derived manifolds (i.e. zero sets of smooth functions)? This is true for schemes and derived schemes, so it seems likely to be the case as principal derived manifolds are "affine" objects.

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    $\begingroup$ Since Spivak's affine derived manifolds are defined to be your principal derived manifolds, you could just take the homotopy colimit of a Cech nerve. I don't see how you can get arbitrary derived schemes, though. $\endgroup$
    – Jon Pridham
    Commented Jun 27, 2019 at 19:33

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