I guess whether "creates" limits depends on whether those limits exist from before or after you observe them.

Hi, the wording of "in what sense" is a bit vague so I'm going to interpret your question as why have the English words "lift", "create" and "detect" ...

Hi, correct me if I'm wrong but I think what's going on here is two theories are Morita equivalent (see TST, pg. 59), at least when restricted to mode...

Hi Matteo, your account on the geometric morphisms is correct (since the essential part is left exact). Then I'm a little confused by your colimit ...