??so what about something about "frankenstein doctrine" ?? ... ??semi-monoidal ... every object is idempotent ... filteredly cocomplete ... ??anything else ??? ...

...hmmm...

something about taking the idempotent objects... from an ag theory or something, i mean... ???or just the "good" ones?? ??or something??? ???better than flat ??? ...??or what ???...

??we _did_ sort of think about stuff a bit like this before... in connection with comparing invertible to idempotent, and so forth ... ??maybe trying to find common generalization, or something ?? ... and so forth ... ??but didn't have these "filtered colimit" ideas back then ?? ... ??or something??? ...

??something about ... ??"categorified semi-lattice of basic affine opens" ... ??or something ?? ... and so forth ...

(??what _about_ something about "site as sort of like categorified basis" or something, and something about ... basis of affine opens for small zariski ... and so forth ... ??...)

??what about something about ... ???categorified "lattice-ordered abelian group" here ???? .... ????or something ??? ....


??something about ... ???"semipro-monoidal" or something ????? .... ???maybe ... "pro-unital semi-monoidal ..." ... ??or something ??? .... ??exept maybe ... something about ... ??"filteredly cocomplete analog of pro" ??? ... ??? or something ??? .... ?????....