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Commutator theory in strongly protomodular categories. (English) Zbl 1068.18006

The paper consists of seven parts. After the introduction the unital and Mal’cev categories are investigated. The fourth paragraph is devoted to normal subobjects, while the next one deals with commutators in pointed finitely cocomplete regular Mal’cev categories. In the last two items the protomodular and strongly protomodular categories are studied. Among other results it is shown that in strongly protomodular categories (in the category of groups especially) the commutator of two equivalence relations coincides with the commutator of their associated normal subobjects.

MSC:

18C99 Categories and theories
08B05 Equational logic, Mal’tsev conditions
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18D30 Fibered categories
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