Data di Pubblicazione:
2012
Citazione:
Action accessibility via centralizers / A.S. Cigoli, S. Mantovani. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 216:8-9(2012 Aug), pp. 1852-1865. [10.1016/j.jpaa.2012.02.023]
Abstract:
In this paperwefirst introduce a non-symmetric notion of centralization between a relation
S and an equivalence relation R, which coincides with Smith centralization in the case S is an
equivalence relation too. We then prove that in any action accessible category in the sense
of Bourn and Janelidze (2009) [11], the centralizer of an equivalence relation R, defined
as in [11], actually has a stronger property, namely it is an equivalence relation, which is
the largest among all the relations S centralizing R in the non-symmetric sense mentioned
above. As a main result, we show that the existence of centralizers for any equivalence
relation with this stronger property actually characterizes action accessibility for exact
protomodular categories.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
A.S. Cigoli, S. Mantovani
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