Buss and Meyer define fibrations of topological groupoids and interpret a groupoid fibration L --> H with fibre G as a generalised action of H on G by groupoid equivalences. My result shows that a generalised action of H on G may be transported along a Morita equivalence G ~ K to a generalised action of H on K, which is given from a fibration R --> H with fibre K. Furthermore, topological groupoids R and L are Morita equivalent.
Keywords: topological groupoid, Morita equivalence, groupoid fibration, generalised groupoid action, fibre of a groupoid fibration
2020 MSC: 22A99
Theory and Applications of Categories, Vol. 35, 2020, No. 41, pp 1549-1563.