We call a finitely complete category algebraically coherent if the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdorff algebras over a semi-abelian algebraically coherent theory. We study equivalent conditions in the context of semi-abelian categories, as well as some of its consequences: including amongst others, strong protomodularity, and normality of Higgins commutators for normal subobjects, and in the varietal case, fibre-wise algebraic cartesian closedness.

Algebraically coherent categories / A.S. Cigoli, J.R.A. Gray, T. Van der Linden. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 30(2015 Dec 08), pp. 1864-1905.

Algebraically coherent categories

A.S. Cigoli
Primo
;
2015

Abstract

We call a finitely complete category algebraically coherent if the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give examples of categories satisfying this condition; for instance, coherent categories, categories of interest in the sense of Orzech, and (compact) Hausdorff algebras over a semi-abelian algebraically coherent theory. We study equivalent conditions in the context of semi-abelian categories, as well as some of its consequences: including amongst others, strong protomodularity, and normality of Higgins commutators for normal subobjects, and in the varietal case, fibre-wise algebraic cartesian closedness.
category of interest; coherent functor; compact Hausdorff algebra; semi-abelian locally algebraically cartesian closed category; Smith, Huq, Higgins commutator; mathematics (miscellaneous)
Settore MAT/02 - Algebra
8-dic-2015
http://www.tac.mta.ca/tac/volumes/30/54/30-54.pdf
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/358350
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