DECIDABLE (EQUALS SEPARABLE) OBJECTS AND MORPHISMS IN LEXTENSIVE CATEGORIES

After investigating all conceivable properties of decidable objects an d maps in left exact categories with well-behaved finite sums ('lexten sive categories'), we give a characterization in such categories of de cidable morphisms which are (finite) coverings (in an appropriate sens e). Finally, we give two applications of this result, to separable alg ebras and to local homeomorphisms. In both cases it explains categoric ally the advantage of two well-known notions - strongly separable alge bras and local homeomorphisms with path lifting property, respectively .