Quotients of decidable objects (${\mathcal{E}}_{qd}$)

In a Grothendieck topos, an object is a quotient of a decidable object when it has an epic cover by one. These objects are closed under subobjects, small coproducts, quotients and finite limits. Their union inside any fixed object gives the largest subobject of this kind, defining a coreflective subcategory. The induced idempotent comonad is left exact, so the full subcategory is a topos.