nLab
smooth (infinity,1)-algebra

Contents

Idea

The notion of smooth (,1)(\infty,1)-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.

Definition

A smooth \infty-algebra is an ∞-algebra over an (∞,1)-algebraic theory TT for TT the ordinary Lawvere theory of smooth algebras.

Properties

The model structure on simplicial algebras on simplicial C-∞-ring is a presentation for smooth (,1)(\infty,1)-algebras.

Applications

Smooth (,1)(\infty,1)-algebras appear as the algebras of functions in derived differential geometry, for instance onderived smooth manifolds.

Revised on January 12, 2012 19:18:35 by Urs Schreiber (195.37.209.182)