On closure operators and reflections in Goursat categories
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2007
- DOI:
- 10.48550/arXiv.0712.0890
- arXiv:
- arXiv:0712.0890
- Bibcode:
- 2007arXiv0712.0890B
- Keywords:
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- Mathematics - Category Theory;
- 18C05;
- 54B30;
- 08B05
- E-Print:
- 14 pages. Accepted for publication in "Rendiconti dell'Istituto Matematico di Trieste"