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Title: A criterion for reflectiveness of normal extensions
Authors: Montoli, Andrea
Rodelo, Diana
Van der Linden, Tim
Keywords: Categorical Galois theory; admissible Galois structure; central, normal, trivial extension; S-protomodular category; unital category; abelian object.
Issue Date: 2016
Publisher: Belgium Mathematical Society - Project Euclides
Project: UID/MAT/00324/2013 
Serial title, monograph or event: Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume: 23
Issue: 5
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.
DOI: 10.36045/bbms/1483671620
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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