In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.

Quotes

• The purpose of sheaf theory is quite general: it is to obtain global information from local information, or else to define “obstructions” which characterize the fact that a local property does not hold globally any more: for example a manifold is not always orientable, or a differential equation can be locally solvable, but not globally.
  • Masaki Kashiwara; Pierre Schapira (1 May 2002). Sheaves on Manifolds: With a Short History. Springer Science & Business Media. p. 1. ISBN 978-3-540-51861-7. 

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