Sheaf of connection algebras

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

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