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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 funcion 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.
- Dennis Borisov, Justin Noel, Simplicial approach to derived differential manifolds (arXiv:1112.0033)
Revised on January 12, 2012 19:19:59
by Urs Schreiber