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december 2016 A criterion for reflectiveness of normal extensions
Andrea Montoli, Diana Rodelo, Tim Van der Linden
Bull. Belg. Math. Soc. Simon Stevin 23(5): 667-691 (december 2016). DOI: 10.36045/bbms/1483671620

Abstract

We give a new sufficient condition for the normal extensions in an admissible Galois structure to be reflective. We then show that this condition is indeed fulfilled when $\mathbb{X}$ is the (protomodular) reflective subcategory of $\mathcal{S}$-special objects of a Barr-exact $\mathcal{S}$-protomodular category $\mathbb{C}$, where $\mathcal{S}$ is the class of split epimorphic trivial extensions in $\mathbb{C}$. Next to some concrete examples where the criterion may be applied, we also study the adjunction between a Barr-exact unital category and its abelian core, which we prove to be admissible.

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Andrea Montoli. Diana Rodelo. Tim Van der Linden. "A criterion for reflectiveness of normal extensions." Bull. Belg. Math. Soc. Simon Stevin 23 (5) 667 - 691, december 2016. https://doi.org/10.36045/bbms/1483671620

Information

Published: december 2016
First available in Project Euclid: 6 January 2017

zbMATH: 06682396
MathSciNet: MR3593569
Digital Object Identifier: 10.36045/bbms/1483671620

Subjects:
Primary: 11R32 , 18F30 , 19C09 , 20M32 , 20M50

Keywords: $\mathcal{S}$-protomodular category , abelian object , admissible Galois structure , categorical Galois theory , central, normal, trivial extension , unital category

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 5 • december 2016
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