On closure operators and reflections in Goursat categories

Borceux, Francis;Gran, Marino;Mantovani, S.
(2007) Universita degli Studi di Trieste. Istituto di Matematica. Rendiconti — Vol. 39, p. 87-104 (2007)

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  • Borceux, FrancisUCLouvain
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  • Gran, MarinoUCLouvain
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  • Mantovani, S.I-MILAN
    Author
Abstract
By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijec- tive correspondence between these closure operators and the regu- lar 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 pro- vide an explicit description of the closure, and to characterise the congruence distributive Goursat categories.
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Borceux, F., Gran, M., & Mantovani, S. (2007). On closure operators and reflections in Goursat categories. Universita degli Studi di Trieste. Istituto di Matematica. Rendiconti, 39, 87-104. https://hdl.handle.net/2078.5/73370 (Original work published 2007)