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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
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Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Quotient crossed module · double groupoid · quotient double groupoid
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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Cite This Article
MUCUK, O., DEMİR, S. (2018). Normality and quotient in crossed modules over groupoids and double groupoids. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 5, 2336–2347. https://ajindex.com/articles/253820