?? idea that borger described about what "schemes" (??? ...) should really be like ... i'd been sort of trying to remember / understand how that went .... todd described it in interestingly suggestive way .... "...modding out by zariski-open equivalence relation" .... ??? .... ???maybe tying in with recent ideas .... ?????.....

??had vague idea that this might make category of such "schemes" something like a quasitopos ... ??? .... (??just because of idea of "getting quasitopos from geometric morphism of toposes" ??? ....) ... ??seems not quite correct now, but ... ???.....

???generalizing from equivalence relation to groupoid here .... ???? ......

"locally ... " .... ???.....

???remembering to try to get involved both "constraining glueing to involve only open inclusions / local isomorphisms" (???...) and "grothendieck topology relating to open inclusions / local isomorphisms" .... ???? ...... ???? ....

???grothendieck topology involved at some sort of _initial_ stage ???? ..... ???then .... ????coequalizer of open equivalence relation ??? .... ????..... ???? .... ???? not sure that makes much sense yet ... i should check again how todd phrased it ... ?? ... hmmm, or did i really copy that down .... ???? ..... ???or were they really just saying more or less what i was trying to say ???? .... ... image subcategory .... ???? .....

????or ... somehow also getting involved idea about ... ???grothendieck topology arising from parameterized model, or from "defective imitation" of such ..... ????? ..... ????? ......

????hmmmm.... ?????trying to understand all (??...) stages of artin / borger / todd idea in context of "image of globalization process adjoint to restricted yoneda embedding" ??? ...... ????? ...... ????

?????also trying to get "combined doctrine" idea involved here ???? ...... ???? ....

?? anyway, let me try pursuing some ideas here a bit ....

?? suppose that f : x -> y is a functor ... ??secretly i'm thinking of an example where y is some sort of category of "spaces" and y is an essentially surjective but non-full subcategory where the morphisms are something like "local isomorphisms" ... i could try to describe even more secret levels that i'm at least vaguely conscious of, but i'll leave it at that for now ....

then ... f_* : _pre-stack_(x) -> _pre-stack_(y) .... ???? ....

??? non-left exact left adjoint ... ???? ..... ????.....