TURKISH JOURNAL OF MATHEMATICS, cilt.45, sa.3, ss.1407-1417, 2021 (SCI-Expanded)
In this work we introduce lifting and covering of a crossed module in the category of group-group oids; and then we prove the categorical equivalence of horizontal actions of a double group-group oid and lifting crossed modules of corresponding crossed module in group-group oids. These allow us to produce more examples of double group-groupoids.