In mathematics, the gluing axiom is introduced to define what a sheaf on a topological space must satisfy, given that it is a presheaf, which is by definition a contravariant functor to a category which initially one takes to be the category of sets. Here is the partial order of open sets of ordered by inclusion maps; and considered as a category in the standard way, with a unique morphism if is a subset of , and none otherwise. is the subset of With equal image in and .
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