?? so ... ??? trying to use gabriel-ulmer duality and / or "currying" to get bi-quasicoherent sheaves as ag correspondences to work nicely ... ??? .... (?? and / or find limitations on how nicely they can work ... ?? ...)

?? egger's stuff about free cocomplete semilattices as being compact whereas more general cocomplete semilattices only being star-autonomous (??? .... again, having trouble with details here ... not sure how helpful my notes for that discussion will be ... ?? ...) as maybe very relevant here ???? ..... hmmmm .... ??? .... ??? could screw things up ?? ... ?? ...

?? getting all original colimit weights to be absolute, vs also getting all the newly introduced ones to be so ... ?? ..

??? again, what sort of dual / adjoint is involved in absoluteness of colimits ?? ??? any conflict between jeff egger's story and richard what's-their-name's story ?? ... ?? ...

? hmm, actually the notes from the discussion with egger seem reasonably helpful ... ?? but page 5 for example does suggest some potential for me to get confused by level slips here ... ?? ...