# Schreiber C-infinity module

Recalling that a C-infty algebra $A$ is a copresheaf $A \in Quantities = CoPrSh(CartesianSpaces)$ which becomes a copresheaf with values in algebras when restricted along $FinSet \hookrightarrow CartesianSpaces$, the idea is to define a smooth module over a C-infinity algebra $A$ to be a copresheaf $N \in Quantities$ which becomes a copresheaf of modules over the copresheaf of algebras $A$ when restricted along $FinSet \to CartesianSpaces$.

# Definition

A $C^\infty$-module over a C-infinity algebra $A$ is a co-presheaf $N \in Quantities = CoPr(CratesianSpaces)$ such that restricted along $FinSet \hookrightarrow CartesianSpaces$ it becomes a copresheaf of modules over the copresheaf (on $FinSet$) of algebras $A$.

# References

(…expand on this….)

# Open issues

• the details of the definition of tensor product of $C^\infty$-modules over $C^\infty$-algebras;

• the details of the definition of dual modules. I.e. with $N$ a \$$C^\infty$-module over the $C^\infty$-algebras $A$, what can we say about

$N^* := Hom_{C^\infty Mod}(N,A) \,.$

For instance: what notion of hom do we use, how do we equip the extra structure?

Last revised on December 10, 2008 at 13:10:04. See the history of this page for a list of all contributions to it.