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.

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.

Action accessibility via centralizers

A.S. Cigoli
Primo
;
S. Mantovani
Ultimo
2012

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.
Settore MAT/02 - Algebra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/177810
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