Crossed squares, crossed modules over groupoids and cat1−2−groupoids

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Crossed squares, crossed modules over groupoids and cat$^{bf {1-2}}-$groupoids

The aim of this paper is to introduce the notion of cat$^{bf {1}}-$groupoids which are the groupoid version of cat$^{bf {1}}-$groups and to prove the categorical equivalence between crossed modules over groupoids and cat$^{bf {1}}-$groupoids. In section 4 we introduce the notions of crossed squares over groupoids and of cat$^{bf {2}}-$groupoids, and then we show their categories are equivalent....

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A. M. S. Classification: 18G30, 18G55.

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ژورنال

عنوان ژورنال: Categories and General Algebraic Structures with Application

سال: 2020

ISSN: 2345-5853,2345-5861

DOI: 10.29252/cgasa.13.1.125