categorified gabriel-ulmer duality and meta-sketching of doctrines

since a doctrine (in my current usage) is a categorified version of a finite limits theory, and since finite limits theories can be "sketched", doctrines can also be sketched, in a slightly categorified way that i'll refer to for now as "meta-sketching". moreover it seems instructive to actually meta-sketch a bunch of examples of doctrines, some toy examples as well as some examples closer to being actually relevant.