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Transfer of a generalised groupoid action along a Morita equivalence

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Giorgi Arabidze

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.

Published 2020-09-10.

http://www.tac.mta.ca/tac/volumes/35/41/35-41.pdf

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