Non-pointed strongly protomodular theories
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.
scientific article; zbMATH DE number 2128567