By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories L of C. When C is an exact Goursat category this correspondence restricts to a bijection between the Birkhoff closure operators on effective equivalence relations and the Birkhoff subcategories of C. In this case it is possible to provide an explicit description of the closure, and to characterise the congruence distributive Goursat categories.
On closure operators and reflections in Goursat categories / F. Borceux, M. Gran, S. Mantovani. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 39:(2007), pp. 87-104.
On closure operators and reflections in Goursat categories
S. MantovaniUltimo
2007
Abstract
By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories L of C. When C is an exact Goursat category this correspondence restricts to a bijection between the Birkhoff closure operators on effective equivalence relations and the Birkhoff subcategories of C. In this case it is possible to provide an explicit description of the closure, and to characterise the congruence distributive Goursat categories.
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