Non-pointed strongly protomodular theories
type: Item
instance of: scholarly article
title: Non-pointed strongly protomodular theories
zbMATH Open document ID: 1063.18001
published in: Applied Categorical Structures
publication date: 2005-01-17T00:00:00Z
review text: The notion of strong protomodularity was introduced to `bridge the gap' between semi-abelian categories (pointed protomodular Barr-exact categories) and the `Moore categories' introduced by \textit{M. Gerstenhaber}: every Moore category is semi-abelian but not conversely, and strong protomodularity is precisely the strengthening of protomodularity required to make the implication reversible. Relatively little work has so far been done on strong protomodularity outside the pointed context: in particular, we do not have a `Mal'cev-type condition' for a variety of algebras to be strongly protomodular, in contrast to the situation for `mere' protomodularity. This paper does not solve that problem, but it gives a sufficient condition for a variety to be strongly protomodular, and uses it to show that various familiar protomodular varieties (rings, \(C^*\)-algebras, Heyting algebras, \dots) are indeed strongly protomodular.
reviewed by: Peter Johnstone
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 18D35
zbMATH DE Number: 2128567
zbMATH Keywords: Strongly protomodular category
zbMATH Keywords: semi-Abelian category
zbMATH Keywords: normal subobject
zbMATH Keywords: \(\mathbb C^*\)-algebra
zbMATH Keywords: ring
zbMATH Keywords: Boolean algebra
zbMATH Keywords: Heyting algebra
author: F. Borceux
MaRDI profile type: Publication
full work available at URL: b:apcs.0000040554.75066.cc
OpenAlex ID: W2072656954
DOI: 10.1023/B:APCS.0000040554.75066.CC
Recommended article: Remarks on strong nonstructure theorems
Recommended article: Q5693583
Recommended article: Pointed protomodularity via natural imaginary subtractions
Recommended article: Constructing strongly equivalent nonisomorphic models for unsuperstable theories, Part A
Recommended article: Constructing strongly equivalent nonisomorphic models for unsuperstable theories, Part C
Recommended article: Constructing strongly equivalent nonisomorphic models for unsuperstable theories. Part B
Recommended article: On a strengthening of the non-isomorphism theorem for provability algebras
Recommended article: Q3787988
Recommended article: Pointwise definable models of set theory
description: scientific article; zbMATH DE number 2128567