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Group-groupoid actions and liftings of crossed modules (1601.07096v1)
Published 26 Jan 2016 in math.CT and math.AT
Abstract: The aim of this paper is to define the notion of lifting of a crossed module via a group morphism and give some properties of this type of the lifting. Further we obtain a criterion for a crossed module to have a lifting of crossed module. We also prove that the liftings of a certain crossed module constitute a category; and that this category is equivalent to the category of covers of that crossed module and hence to the category of group-groupoid actions of the corresponding groupoid to that crossed module.
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