A criterion for reflectiveness of normal extensions

Montoli, Andrea; Rodelo, Diana; Van der Linden, Tim

http://hdl.handle.net/10400.1/9668

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Authors

Montoli, Andrea

Rodelo, Diana

Van der Linden, Tim

Abstract(s)

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.