| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 794.75 KB | Adobe PDF |
Orientador(es)
Resumo(s)
The aim of this work is to study the notions of lax protomodular and Ord-Mal’tsev category at the level of (coherent) varieties of (pre)ordered algebras and to further compare them, as has been done in the non-ordered context. We characterise varieties of ordered algebras which are (co)lax protomodular and those which are Ord-Mal’tsev, in terms of operations of arities given by ordered sets and inequalities involving them. We exhibit examples of (co)lax protomodular non-degenerate Ordcategories, which were unknown. We prove that, for varieties of ordered algebras which are Ord-Mal’tsev categories, the order of their algebras is degenerate (i.e. is symmetric). As a consequence, the implication ``protomodular ⇒ Mal’tsev'' cannot be carried out to our context. The case of non-coherent ordered varieties which are Ord-Mal’tsev categories is also addressed, where we show the existence of algebras with non-degenerate order.
Descrição
Palavras-chave
Categories enriched in the category of preorders Mal’tsev categories. Varieties of ordered algebras Mal’tsev operation
Contexto Educativo
Citação
Editora
Elsevier BV