nLab
derived smooth manifold

Contents

Idea

A derived smooth manifold is a structured generalized space given by a manifold whose structure sheaf of “smooth functions” is a higher categorical generalized smooth algebra.

Definition

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References

Derived smooth manifolds were defined in

  • David Spivak, Quasi-smooth derived manifolds, PhD thesis, Berkeley (2007) (pdf)

This original version of the PhD thesis essentially looks at structured (∞,1)-toposes of ∞-stacks on a topological space for the pregeometry given by 𝒯= Diff.

The published version

essentially does the same, but with Diff replaced by CartSp. Only that CartSp does not quite satisfy all the axioms of a pregeometry.