In mathematics, a sheaf is a tool for systematically tracking locally defined data
attached to the open sets of a topological space.
The data can be restricted to smaller open sets, and
the data assigned to an open set is equivalent to all collections of compatible data
assigned to collections of smaller open sets covering the original one.
For example, such data can consist of the rings of continuous or
smooth real-valued functions defined on each open set.
Sheaves are by design quite general and abstract objects, and
their correct definition is rather technical.
They are variously defined, for example, as sheaves of sets or sheaves of rings,
depending on the type of data assigned to open sets.
|