nLab
simplicial C-infinity-ring

Contents

Definition

A simplicial C C^\infty-ring is a simplicial object in the category of C∞-rings.

Applications

When equipped with the model structure on simplicial algebras over the Lawvere theory CartSp, simplicial C C^\infty-rings are a model for smooth (∞,1)-algebras, hence for (,1)(\infty,1)-algebras over CartSp regarded as an (∞,1)-algebraic theory.

Therefore, in higher analogy to how C C^\infty-rings serve as funcion algebras on smooth loci in differential geometry, so simplicial C C^\infty-rings serve as function rings on derived smooth manifolds and more general spaces in derived differential geometry.

References

  • Dennis Borisov, Justin Noel, Simplicial approach to derived differential manifolds (arXiv:1112.0033)

Revised on January 12, 2012 19:19:59 by Urs Schreiber (195.37.209.182)