Mal’tsev and Lawvere functors. (English) Zbl 1482.18002
Summary: We investigate, at the level of functors, the effect of definitions mimicking those of Mal’tsev and naturally Mal’tsev categories, and show that they give rise to the same kind of characterizations. We give, among others, an application concerning the characterization of the Smith=Huq condition.
MSC:
| 18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms |
| 08C05 | Categories of algebras |
| 18A32 | Factorization systems, substructures, quotient structures, congruences, amalgams |
| 18E13 | Protomodular categories, semi-abelian categories, Mal’tsev categories |
| 08B10 | Congruence modularity, congruence distributivity |
Keywords:
internal groupoids; Mal’tsev; naturally Mal’tsev and protomodular categories; \(\Sigma\)-Mal’tsev categories; centralization of equivalence relations; Smith=Huq conditionReferences:
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