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.
Citation
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