nLab
canonical topology

The canonical topology on a category $C$ is the Grothendieck topology on $C$ which is the largest subcanonical topology. More explicitly, a sieve $R$ is a covering for the canonical topology iff every representable functor is a sheaf for every pullback of $R$. Such sieves are called universally effective-epimorphic.

If $C$ is a Grothendieck topos, then the canonical covering sieves are those that are jointly epimorphic. Moreover, in this case the canonical topology is generated by small jointly epimorphic families, since $C$ has a small generating set. The canonical topology of a Grothendieck topos is also special in that every sheaf is representable; that is, $C\simeq \mathrm{Sh}(C)$.