Presheaf
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Let be a topological space.

A presheaf (of sets) on is a contravariant functor from the category of open subsets of and inclusions to the category of sets.

1. A presheaf of sets on is a rule which assigns to each open a set and to each inclusion a map such that and whenever we have .

2. A morphism of presheaves of sets on is a rule which assigns to each open a map of sets compatible with restriction maps, i.e., whenever are open the diagram

commutes.

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