??? was going to suggest defining object as "essential" iff "not a filtered colimit in a non-trivial way" (???) and/or "homming from it preserves filtered colimits" .... ??? but various weird things about this?? ... ???analogy connected : sums :: propsed "essential" : filtered colimits ... ??? but "connected" here as tending to occur in cocomplete (???.... ????....) context ... ???.... (??... ???trying to apply "connected" in context where you just have sums, and proposed "essential" in context where you just have filtered colimits ??? .... ?????also ... ???how flatness of co-presheaf reduces to ...???... when site category has ...???... ??????) ??also ... ?? dual cones of fan for projective line, for example .... ???? .... ????.... ??not seeming to fit together ?? ... ???? ....

???possibility that "homming from it preserves filtered colimits" is right here, while "not a filtered colimit in a non-trivial way" is not quite right in general ???? ...... ?????? .....

??well, so let's try checking whether "homming out of it preserves filtered colimits" relates in interesting (??) way to original (???...) sense of "essential" ... ???...

??? model (... in "diaconescu" case ... ???? ... ???just how relevant _is_ this case??? .... ... ??? "generalized diaconescu" ??? .... ???? ....) as "flat co-presheaf" .... essential model as "arbitrarily flat" ???? .... ????.... tensoring presheaves with it as preserving not just finite limits, but arbitrary ones ... ????.... ???so that a left adjoint to such tensoring exists ???? .....

???_any_ relationship between ..... ???? ..... "object x in filteredly cocomplete category c is such that homming from it preserves filtered colimits" and "co-presheaf on c given by homming out of x is such that tensoring it with presheaves preserves filtered colimits" ???? ..... ?????? ....... ???????.....





??relationship between essentialness of model and ... ???how treated by "generalized yoneda embedding" ??? .... ??? ....


???"flatness of co-presheaf wrt a class of diagram schemes" .... ????as maybe reducing to something when the site category has (???co- ???)limits of that kind ... ???? ..... ????....

??? "preserve limits of actual objects vs of virtual objects" .... ??? ... when virtual case reduces to actual case .... ????.....

???? .... "it itself vs tensoring with it" ..... ????..... ???? "it itself" here sort-of as ... ???? ???homming out of it ???? .....???? ??does that make any sense ?????? ..... object .... co-presheaf ..... ?????? .......


??? yoneda embedding : flat :: "generalized yoneda embedding" : ?? ..... ???????.....



???!!!try to straighten this (???) out ..... ??????......



???"to preserve existing x-limits among actual objects as necessary for x-flatness (of... ??...), and sufficient if all such x-limits exist ..." .... ????....