Normality and quotient in crossed modules over groupoids and double groupoids
Osman Mucuk, Serap Demir
TL;DR
This paper explores the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures, analyzing how concepts of normality and quotient relate within these frameworks and providing illustrative examples.
Contribution
It establishes the relationship between normality and quotient concepts in crossed modules over groupoids and double groupoids, enriching the understanding of their categorical equivalence.
Findings
Normality and quotient concepts are related in both categories.
Examples illustrating these objects are provided.
Categorical equivalence is used to connect the concepts.
Abstract
We consider the categorical equivalence between crossed modules over groupoids and double groupoids with thin structures; and by this equivalence, we prove how normality and quotient concepts are related in these two categories and give some examples of these objects.
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