??trying to reconcile (??...) certain approaches (??...) to "doctrine as special case of 2-topos" ....

1 : ???... "theory as 2-formula and environment as 2-model" ... ??...

2 : ??... categorification of [lex theory as special case of topos] ...

???maybe these can be reconciled fairly well if ... ??just remember ... ??2-topos has more 2-formulas than corresponding 2-doctrine does ... ...?? "syntactic (2,1)-category" .... groupoid-valued (2,1) functors on syntactic 2-category of doctrine as giving syntactic 2-category of 2-topos .... ?????only the representable (??maybe expressed in terms of weak limit preservation ... ???? ...???..) such functors preserving filtered (????...) weak colimits as being in the syntactic 2-category of the doctrine??? ....

??so maybe these two approaches really are practically the same ??? ....

what got me thinking about this today was mostly, i think, talking with alex yesterday... ???....question as to what kind of parallelism (??or "tweisted" such ??c ...) there is in ... "doctrine made up of theories, each in turn made up of formulas ..." (???...) ... ?????.....

??? ... ???working out uncategorified "lex theory as special case of topos" ... ???to what extent / when have we done this ?? .... ??? ...... ?????.....