?? what happens to idea of superman-flavor equivalence between _nice TAG theory_ (in form of accidental topos ... ??? ...) and _nice AG theory with extra toric convolution tensor product_ when ... ??? the first tensor product is omitted, or perhaps identified with the extra one ?? .....

?? encoding topos as special kind of AG theory, from which it can be recovered by taking the nice comonoids in the AG theory ??? .....

??construing above as special case of encoding ringed topos as AG theory ... ???? .... from which it can be recovered by taking the nice comonoids, and taking the special ring object to be the unit-object-as-coalgebra ... ?? afterwards can ask whether the ring object is "the integers", which is supposed to tell you that it's the original special case .... ???....

?? relative toric variety .... ??? ....



?? this original special case as distinguishing the toric convolution product from the "first" tensor product ??? .... ???? .... ????? ...... ??????? ........ .........

??? abstract generalization (?? ...) of "small zariski topos" here ????? ...... ??? .... ?? "spectrum" in tierney/johnstone sense ??? .... ???? ....

??? quasicoherence here (?? ...) ?? .....

?? nice coalgebras of a commutative ring ......for example nice coalgebras of k[x] .... ???? .... ?? given an object s in the small zariski topos of a commutative ring r .... try to get nice coalgebra of r .... ????? .... ?? take free r'-module on s where r' is the "structure sheaf" .... ?? _will_ this generally be quasicoherent ??? ..... i think no, but don't really remember at the moment how this works .... ??? .... hmmmm ......

?? "quasicoherentization" ... ??? ...

?? possibility we had the right idea above only up to the point where we tried generalizing from topos to ringed topos .... ???? ....