A criterion for reflectiveness of normal extensions

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 cla...

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Bibliographic Details
Main Author: Montoli, Andrea (author)
Other Authors: Rodelo, Diana (author), Van der Linden, Tim (author)
Format: article
Language:eng
Published: 2016
Subjects:
Categorical Galois theory; admissible Galois structure; central, normal, trivial extension; S-protomodular category; unital category; abelian object.
Online Access:http://hdl.handle.net/10316/89489
Country:Portugal
Oai:oai:estudogeral.sib.uc.pt:10316/89489
Description
Summary: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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