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arXiv · 1602.02515

A criterion for reflectiveness of normal extensions

Andrea Montoli·Diana Rodelo·Tim Van der Linden
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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 X is the (protomodular) reflective subcategory of S-special objects of a Barr-exact S-protomodular category C, where S is the class of split epimorphic trivial extensions in 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. 2016-02-08. A criterion for reflectiveness of normal extensions. https://arxiv.org/abs/1602.02515

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