In fact, more is true: as discussed there in detail, in the projective local model structure on simplicial presheaves on Diff there is a cofibrant resolution functor with values in simplicial manifolds. (Here we allow Diff to be closed under coproducts indexed by sets; that is, we do not require our manifolds to be connected or second-countable, although we may require their components to be second-countable). Therefore every ∞-stack on Diff may be presented by a simplicial manifold.

Last revised on January 14, 2017 at 03:56:41.
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