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On Closure Operators and Reflections in Goursat Categories
Borceux, F.
Gran, M.
Mantovani, S.
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Publisher
EUT Edizioni Università di Trieste
Source
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.
Languages
en
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