An effective congruence is a congruence. If X is a set in Set , a subset U of X 2 is a congruence iff it is an equivalence relation on X . Any intersection of congruences is a congruence. This follows from the fact that the classes of equavelnce relations and closed subsets are closed under intersections. Any intersection of effective congruences is an effective congruence.
G be the generic extensiion of q .
Suppose V is another effective congruence on X containing U . U i for any U i . This shows that U is an effective congruence. A variety is an algebraic category such that any congruence is effective.