We clarify the relationship between basic constructions of semi-abeliancategory theory and the theory of ideals and clots in universalalgebra. To name a few results in this frame, which establish connections between hitherto separated subjects, 0-regularity in universalalgebra corresponds to the requirement that regular epimorphisms are normal; we describe clots in categorical terms and show that ideals are images of clots under regular epimorphisms; we show that the relationship between internal precrossed modules and internal reflexive graphs extends the relationship between compatible reflexive binary relations and clots.

Janelidze, G., Marki, L., Ursini, A. (2007). Ideals and clots in universal algebra and in semi-abelian categories. JOURNAL OF ALGEBRA, 307(1), 191-208 [10.1016/j.jalgebra.2006.05.022].

Ideals and clots in universal algebra and in semi-abelian categories

Ursini A.
2007-01-01

Abstract

We clarify the relationship between basic constructions of semi-abeliancategory theory and the theory of ideals and clots in universalalgebra. To name a few results in this frame, which establish connections between hitherto separated subjects, 0-regularity in universalalgebra corresponds to the requirement that regular epimorphisms are normal; we describe clots in categorical terms and show that ideals are images of clots under regular epimorphisms; we show that the relationship between internal precrossed modules and internal reflexive graphs extends the relationship between compatible reflexive binary relations and clots.
2007
Janelidze, G., Marki, L., Ursini, A. (2007). Ideals and clots in universal algebra and in semi-abelian categories. JOURNAL OF ALGEBRA, 307(1), 191-208 [10.1016/j.jalgebra.2006.05.022].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/24857
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