Abstract
Abstract
The aim of this paper is to define the notion of lifting via a group morphism for a crossed module and give some properties of this type of liftings.
Further, we obtain a criterion for a crossed module to have a lifting crossed module.
We also prove that the category of the lifting crossed modules of a certain crossed module is equivalent to the category of group-groupoid actions on groups, where the group-groupoid corresponds to the crossed module.
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