Publication
Weakly Mal’tsev Categories and Strong Relations
| Summary: | We define a strong relation in a category C to be a span which is “orthogonal” to the class of jointly epimorphic pairs of morphisms. Under the presence of finite limits, a strong relation is simply a strong monomorphism R → X × Y . We show that a category C with pullbacks and equalizers is a weakly Mal’tsev category if and only if every reflexive strong relation in C is an equivalence relation. In fact, we obtain a more general result which includes, as its another particular instance, a similar well-known characterization of Mal’tsev categories. |
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| Main Authors: | Janelidze, Zurab |
| Other Authors: | Martins-Ferreira, Nelson |
| Subject: | Difunctional relation Factorization system Mal'tsev category Weakly Mal'tsev category |
| Year: | 2012 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade de Leiria e Oeste |
| Language: | English |
| Origin: | IC-online |
| Summary: | We define a strong relation in a category C to be a span which is “orthogonal” to the class of jointly epimorphic pairs of morphisms. Under the presence of finite limits, a strong relation is simply a strong monomorphism R → X × Y . We show that a category C with pullbacks and equalizers is a weakly Mal’tsev category if and only if every reflexive strong relation in C is an equivalence relation. In fact, we obtain a more general result which includes, as its another particular instance, a similar well-known characterization of Mal’tsev categories. |
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