?? idea that [realization pairing between accidental topos formulas and models] as equivalent to [pairing "global sections of tensor product" between toric quasicoherent sheaves and the basic localizations among them] as pretty obvious from certain viewpoint ... ?? that of course (?? ...) the formula-model pairing gives the "basic local sections", and of course (? again, certain viewpoint ... ?? ?? hmm, so maybe obvious from certain simultaneous pair of viewpoints ... ??? ...) the local sections are given by "global sections of tensor product" pairing between quasicoherent sheaves and the special ones given by the basic localizations .... ?? but then there's the issue of what structure on those basic localizations you remember or forget .... ??? and it seems that there's some sort of analogy here .... [more rigid structure on basic localization ...]:[less rigid structure on basic localization]::[accidental geometric morphism ... ?? where "line bundle" phenomenon shows up ... ?? ...]:[semi-monoidal accidental geometric morphism ... where "line bundle" degree of freedom (?? ...) gets rigidified ...] .... ??? .... ??? level slip here between model as object and as morphism (?? "single-variable correspondence" ... ?? ...) ... line bundle ... ?? extra nonrigidity seeping into transition functions .... ??? ..... (?? "stackification" .... ??? .....)


localization of comm monoid (?? or ring ?? ... ???? non-troic analog issue everywhere (?? ...) here ...) .... as .... comonoid (?? and / or "frobenius (??bi-??)monoid" ??? ... ???? ...) in module category ... forgetting vs not forgetting that (?? ...) extra structure ..... ??


??? each object as semi-monoid in the semi-monoidal filteredly cocomplete category .... ??? equivalence between quasicoherent sheaves of actions and filteredly cocontinuous functors here ... ???? .....

?? more (explicit ...) in paper about "ulterior ..." ... ?? ...

?? "single-variable correspondence" ... ??? ....

??? "frobenius" ... "bi-lax" ... ???? .... ??? comonoid vs monoid ... ??? ...some confusion or at least unclarity / ignorance .... ??? ....

??? trying to connect up toric line bundle / accidental geometric morphism connection with "toric proj" / "toric serre's theorem" ??? ....

?? "accidental infinity-topos" idea ... ?? maybe all toric opens get promoted to basic ?? ... ??? ...