Crossed squares, crossed modules over groupoids and cat$^{bf {1-2}}-$groupoids
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Abstract:
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. These equivalences enable us to obtain more examples of groupoids.
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Journal title
volume 13 issue 1
pages 125- 142
publication date 2020-07-01
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