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, 191-208 [10.1016/j.jalgebra.2006.05.022].

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

URSINI, ALDO
2007

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/24857
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