?? catalog of toposes associated to a toric variety ...??or something ....

??all the not-especially-toric ones ...

?? toric mother topos and its daughters ...

"toric small zariski" ... (or something...) ???relationship to mother topos and so forth ... ??

actions of "structure" comm monoid object ... aka "toric non-quasicoherent" ???

torpos ... aka "toric quasicoherent" ...

relationship between these last two ... formal properties of inclusion, and so forth ... ??maybe partially special to toric case, partially not ??...

...other relationships here ... ???...


??perhaps also something about ... ??graded actions ... ??though perhaps not quite fully intrinsic... ??well, though you could try making it intrinsic by "saturation" or something ... ??not quite sure to what extent that works ... ??....