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In this paper a Bass-Serre theory in the groupoid setting is developed and astructure theorem is established. Any groupoid action without inversion ofedges on a forest induces a graph of groupoids, while any graph of groupoidssatisfying certain hypothesis admits a canonical associated groupoid, calledthe fundamental groupoid, and a forest, called the Bass-Serre forest, such thatthe fundamental groupoid acts on the Bass-Serre forest. The structure theoremstates that these processes are mutually inverse.

Bass-Serre theory for groupoids