  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.
