CONSTRUCTING (WEAK) LAWVERE-TIERNEY TOPOLOGIES

In this article, we start with a collection M of morphisms of a category X, that satisfies certain conditions and we construct a subobject M of the subobject classifier ­ in the topos SetXop of presheaves. By classifying this subobject we get a morphism j : ­ ! ­ in SetXop . Finally, we find the equivalent conditions on M rendering j a (weak) Lawvere- Tierney topology.