Author(s): Montoli, Andrea ; Rodelo, Diana ; Van der Linden, Tim
Date: 2016
Persistent ID: https://hdl.handle.net/10316/89489
Origin: Estudo Geral - Universidade de Coimbra
Subject(s): Categorical Galois theory; admissible Galois structure; central, normal, trivial extension; S-protomodular category; unital category; abelian object.
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.
