Could not include topos theory - contents
For a regular category $C$, the regular coverage on $C$ is the coverage whose each covering family has one element which is a regular epimorphism.
The Grothendieck topology generated from a regular coverage is called the regular topology.
subcanonical Grothendieck topology whose covering families are generated by single regular epimorphisms: the regular coverage.
If $C$ is exact or has pullback-stable reflexive coequalizers, then its codomain fibration is a stack for this topology (the necessary and sufficient condition is that any pullback of a kernel pair is again a kernel pair).
For $\mathcal{C}_{\mathbb{T}}$ the syntactic category of a regular theory, the regular coverage makes it the syntactic site, which is a site of defininition for the classifying topos of $\mathcal{T}$.