symmetric monoidal (∞,1)-category of spectra
The notion of smooth -algebra is the analog in higher category theory of smooth algebra. This is the basis for the derived geometry version of differential geometry/synthetic differential geometry.
A smooth -algebra is an ∞-algebra over an (∞,1)-algebraic theory for the ordinary Lawvere theory of smooth algebras.
The model structure on simplicial algebras on simplicial C-∞-ring is a presentation for smooth -algebras.
Smooth -algebras appear as the algebras of functions in derived differential geometry, for instance on derived smooth manifolds.
Last revised on December 2, 2016 at 13:50:42. See the history of this page for a list of all contributions to it.