A PROPERTY OF EFFECTIVIZATION AND ITS USES IN CATEGORICAL LOGIC.

We show that a fully faithful and covering regular functor between regular categories induces a fully faithful (and covering) functor between their respective effectivizations. Such a functor between effective categories is known to be an equivalence. We exploit this result in order to give a constructive proof of conceptual completeness for regular logic. We also use it in analyzing what it means for a morphism between effective categories to be a quotient in the 2-category of effective categories and regular functors between them. [ABSTRACT FROM AUTHOR]