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arXiv · 0712.0890

On closure operators and reflections in Goursat categories

Francis Borceux·Marino Gran·Sandra Mantovani
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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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Francis Borceux, Marino Gran, Sandra Mantovani. 2007-12-06. On closure operators and reflections in Goursat categories. https://arxiv.org/abs/0712.0890

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