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.