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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4104

Title: On Closure Operators and Reflections in Goursat Categories
Authors: Borceux, F.
Gran, M.
Mantovani, S.
Keywords: Closure operators
topological algebras
Mal’tsev and Goursat categories
Birkhoff subcategories
Issue Date: 2007
Publisher: EUT Edizioni Università di Trieste
Citation: F. Borceux, M. Gran, S. Mantovani, "On Closure Operators and Reflections in Goursat Categories”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 39 (2007), pp. 87-104.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Abstract: By defining a closure operator on effective equivalence relations in a regular category $\matcal C$, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories $\matcal L$ of $\matcal C$. When $\matcal C$ 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 $\matcal C$. In this case it is possible to provide an explicit description of the closure, and to characterise the congruence distributive Goursat categories.
URI: http://hdl.handle.net/10077/4104
ISSN: 0049-4704
MS Classification: 18C05
18B30
54B30
08B05
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.39 (2007)

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