It is clear that we are living in very exciting time for topos theory, with many exciting developments from different directions. Of course most notable are Lurie's work on higher categories and Caramello's ''vast extension of Felix Klein's Erlangen Program'', to quote André Joyal himself. However, I have not seen either of these schools adress the other directly, of course this might just be limited experience on my part, but given that both of these directions are clearly of interest for category lovers, geometers and all sorts of other mathematicians, it naturally begs the question: Has there been any work connecting these schools of thought? Could Caramello's program be extended to higher topoi, if not what are the reasons for this? Are there any sources addressing these questions that I have missed? Or is it maybe something to do with the infamous categorical in-fighting?
Naturally this question is naive and might answer itself immediately once one dives into either theory properly, however these theories are difficult to understand for an outsider who might nonetheless be interested in how they could approach these subjects. Concrete references would be greatly appreciated.