nLab
derived differential geometry

Idea

Derived differential geometry is higher differential geometry in an ambient (∞,1)-topos which is not 1-localic. This is the derived geometry corresponding to differential geometry. Typically this is specifically taken to be the derived geometry induced by the Lawvere theory for smooth algebras ($C^\infty$-rings):

See

• smooth (∞,1)-algebra, simplicial C-∞-ring

• derived smooth manifold

• derived critical locus

Related concepts

• synthetic differential geometry

• D-geometry

References

• Urs Schreiber, Seminar on derived differential geometry

• Dominic Joyce, D-manifolds and d-orbifolds: a theory of derived differential geometry (pdf)

• Dominic Joyce, Aarhus Masterclass on Derived Differential Geometry (videos)