??something about ... ???"borrowing colimits from the objects whose spectrums (??wrt some "pairing" or something???...) are being taken", vs ... "deciding that some given colimits (for example of affine schemes or something ...??...) are broken because of not being preserved by certain spectrum process" ... ????and so forth ???

???confusion here about "pairing" vs "functor along which to restrict yoneda embedding" ??? ..

???something about terminology "restricted yoneda embedding" for restricting _value_ functors of yoneda embedding ....

???something about ... ???"spectrum" here (...) as like "yoneda embedding" ... ???something about pretty severe constraint to ask for yoneda embedding to preserve colimits .... ????something about "point-like objects" ???? .... ???something about "field" and "spectrum" thereof .... ????something about "voodoo" ... ??? ... "generic point" ... ...and so forth ...

????something about _various_ special cases of "spectrum" (and so forth ...) idea where one or other of the (...) categories involved is a presheaf topos ... and so forth ... ???something about "isbell conjugation" and _limits_ of presheaves ... and so forth ... ????...

???...limits of commutative monoids .... ??... (2,1)-limits of tag theories ... and so forth ... ???....

???something about "relative" (or something...) geometric morphisms between slice toposes ... and big zariski topos of x as slice topos of big zariski topos of 1 ... and so forth ... ???....

???so what _about_ "open cover" vs "colimit" ??? .... and so forth ... ???....