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A ÿbration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. This paper develops systematically the theory of graph ÿbrations, emphasizing in particular those results that recently found application in the theory of distributed systems.doi:10.1016/s0012-365x(00)00455-6 fatcat:56ylwecaybeydnryzlycqiczam