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arXiv · 1601.07096

Group-groupoid actions and liftings of crossed modules

Osman Mucuk·Tunçar Şahan
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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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Osman Mucuk, Tunçar Şahan. 2016-01-26. Group-groupoid actions and liftings of crossed modules. https://doi.org/10.1515/gmj-2018-0001

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