NON ABELIAN HOMOLOGY AND COHOMOLOGY IN ACTION ACCESSIBLE CATEGORIES

Publicações

Schreier split epimorphisms between monoids

Publication . Bourn, Dominique; Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela

We explore some properties of Schreier split epimorphisms between monoids, which correspond to monoid actions. In particular, we prove that the split short five lemma holds for monoids, when it is restricted to Schreier split epimorphisms, and that any Schreier reflexive relation is transitive, partially recovering in monoids a classical property of Mal'tsev varieties.

2014-03-20Artigo científico

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Semidirect Products and Split Short Five Lemma in Normal Categories

Publication . Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, Manuela

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.

2013-11-28Artigo científico

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Palavras-chave

, Exact sciences ,Exact sciences/Mathematics

Entidade financiadora

Fundação para a Ciência e a Tecnologia, I.P.

Número da atribuição

SFRH/BPD/69661/2010