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research article

Conditional Flatness, Fiberwise Localizations, And Admissible Reflections

Gran, Marino
•
Scherer, Jerome  
June 23, 2023
Journal Of The Australian Mathematical Society

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localization, analogous results to those obtained in the category of groups hold, and we provide existence theorems for certain localization functors in specific semi-abelian categories. We prove that a Birkhoff subcategory of an ideal determined category yields a conditionally flat localization, and explain how conditional flatness corresponds to the property of admissibility of an adjunction from the point of view of categorical Galois theory. Under the assumption of fiberwise localization, we give a simple criterion to determine when a (normal epi)-reflection is a torsion-free reflection. This is shown to apply, in particular, to nullification functors in any semi-abelian variety of universal algebras. We also relate semi-left-exactness for a localization functor L with what is called right properness for the L-local model structure.

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Type
research article
DOI
10.1017/S1446788723000046
Web of Science ID

WOS:001011968700001

Author(s)
Gran, Marino
Scherer, Jerome  
Date Issued

2023-06-23

Publisher

CAMBRIDGE UNIV PRESS

Published in
Journal Of The Australian Mathematical Society
Article Number

PII S1446788723000046

Subjects

Mathematics

•

localization

•

reflector

•

semi-abelian category

•

admissibility

•

categorical galois theory

•

conditional flatness

•

torsion theories

•

galois theory

•

factorization

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
UPHESS  
Available on Infoscience
July 17, 2023
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/199118
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