symmetric monoidal (∞,1)-category of spectra
A simplicial -ring is a simplicial object in the category of C∞-rings.
When equipped with the model structure on simplicial algebras over the Lawvere theory CartSp, simplicial -rings are a model for smooth (∞,1)-algebras, hence for -algebras over CartSp regarded as an (∞,1)-algebraic theory.
Therefore, in higher analogy to how -rings serve as function algebras on smooth loci in differential geometry, so simplicial -rings serve as function rings on derived smooth manifolds and more general spaces in derived differential geometry.
Last revised on December 23, 2016 at 11:03:13. See the history of this page for a list of all contributions to it.