Construction of Closure Operations in a Category of Presheaves

We construct some types of universal closure operations induced by certain collection of morphisms. For this purpose, we use Lawvere-Tierney topologies and universal closure operations that correspond to each other to establish the equivalent conditions over the collection of morphisms. In this way we use multiple sieves instead of principal sieves for constructing results. Examples are also given to illustrate the established results.

Keywords:

Class of Morphisms , Lawvere-Tierney Topology , Closure Operation , Presheaf