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What prompted this question is the definition of a pseudogroup in nlab:

Given a X a topological space. Then a pseudogroup is a subgroupoid of the groupoid of transitions between open sets in X, contains the groupoid of identity transitions, and satisfies a sheaf condition.

(Pseudogroups of continuous/smooth transitions are used to define the atlases for manifolds of the respective kind).

It seems to me a pseudogroup is morally a groupoid G that satisfies the sheaf condition for each presheaf G[-,V] for V an object of G.

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    So a generalisation of a pseudogroup would be, G a groupoid; I turn G into a site by equipping it with a coverage J (that generates a grothendieck topology), then require J to be subcanonical so that every representable hom functor G[-,V] is a sheaf?2012-08-27

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The largest (weakest) Grothendieck topology where all contravariant hom functors are sheaves corresponds to the canonical topology. See: http://ncatlab.org/nlab/show/canonical+topology