On closure operators and reflections in Goursat categories

Details On closure operators and reflections in Goursat categories On closure operators and reflections in Goursat categories

2007-12-06

arxiv.org/abs/0712.0890v1

Mathematics

Category Theory

14 pages. Accepted for publication in "Rendiconti dell'Istituto Matematico di Trieste"

Scientific paper

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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