nLab
derived smooth manifold

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

… just a second …

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

• David Spivak, Derived smooth manifolds (arXiv)

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