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Semidirect Products and Split Short Five Lemma in Normal Categories
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| In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist. | 248.96 KB | Adobe PDF |
Orientador(es)
Resumo(s)
In this paper we study a generalization of the notion of categorical semidirect product, as defined in [6], to a non-protomodular context of categories where internal actions are induced by points, like in any pointed variety. There we define semidirect products only for regular points, in the sense we explain below, provided the Split Short Five Lemma between such points holds, and we show that this is the case if the category is normal, as defined in [12]. Finally, we give an example of a category that is neither protomodular nor Mal’tsev where such generalized semidirect products exist.
Descrição
Palavras-chave
Internal actions Normal categories Regular points Semidirect products
Contexto Educativo
Citação
Martins-Ferreira, N., Montoli, A. & Sobral, M. Semidirect Products and Split Short Five Lemma in Normal Categories. Appl Categor Struct 22, 687–697 (2014). https://doi.org/10.1007/s10485-013-9344-5.
Editora
Springer Nature