nLab covering

• effective epimorphism$\Rightarrow$ regular epimorphism $\Leftrightarrow$ covering

• effective monomorphism$\Rightarrow$ regular monomorphism $\Leftrightarrow$ embedding .

The term “covering” may refer to:

1. in topology:

   covers, such as open covers or covering spaces;

   in which case “covering map” means: “deck transformation”

2. more generally in sheaf and topos theory:

   covering families of a coverage or Grothendieck topology