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arXiv · 1309.3109

Abelian crossed modules and strict Picard categories

Nguyen Tien Quang·Che Thi Kim Phung·Ngo Sy Tung
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Abstract

In this paper, we state the notion of morphisms in the category of abelian crossed modules and prove that this category is equivalent to the category of strict Picard categories and regular symmetric monoidal functors. The theory of obstructions for symmetric monoidal functors and symmetric cohomology groups are applied to show a treatment of the group extension problem of the type of an abelian crossed module.

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Nguyen Tien Quang, Che Thi Kim Phung, Ngo Sy Tung. 2013-09-12. Abelian crossed modules and strict Picard categories. https://arxiv.org/abs/1309.3109

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