Sheaf (mathematics)

In mathematics, a sheaf F on a given topological space X gives a set or richer structure F(U) for each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and gluing smaller open sets to obtain a bigger one. A presheaf is similar to a sheaf, but it may not be possible to glue. Sheaves, it turns out, enable one to discuss in a refined way what is a local property, as applied to a function.

See also

• Gerbe
• Stack (category theory)