Might mean (unverified): Subset closed under restriction maps.
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We found 2 dictionaries that define the word subsheaf:

General (1 matching dictionary)
  1. subsheaf: Wiktionary

Science (1 matching dictionary)
  1. subsheaf: PlanetMath Encyclopedia

Definitions from Wiktionary (subsheaf)

noun:  (mathematics) A subset of a sheaf

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