A characterisation of the “Smith is Huq” condition in the pointed Mal’tsev setting. (English. French summary) Zbl 1301.18005
Summary: We give a characterisation of the “Smith is Huq” condition for a pointed Mal’tsev category \(\mathbb{C}\) by means of a property of the fibration of points \(¶_{\mathbb{C}}:\mathrm{Pt}(\mathbb{C})\to\mathbb{C}\), namely: any change of base functor \(h^\ast:\mathrm{Pt}_Y(\mathbb{C})\to\mathrm{Pt}_X(\mathbb{C})\) reflects commuting of normal subobjects.
MSC:
| 18A20 | Epimorphisms, monomorphisms, special classes of morphisms, null morphisms |
| 08B05 | Equational logic, Mal’tsev conditions |
| 18D35 | Structured objects in a category (MSC2010) |
| 54H11 | Topological groups (topological aspects) |
