# Sheaf of connection algebras

This article defines a sheaf that can be associated to a differential manifold. The global analog of this sheaf, which is also the same as the object of the sheaf associated to the whole manifold, is:connection algebra

## Definition

Let be a differential manifold. The **sheaf of connection algebras** of is defined as follows:

- For every open subset of , the object associated to is the connection algebra associated to , viewed as a manifold.
- The restriction map is defined using the natural restriction map for the sheaf of first-order differential operators, and the sheaf of infinitely differentiable functions

Sometimes the **sheaf of connection algebras** is termed the connection algebra, though the latter term is sometimes used for the *global object*.