??my naive "explosion" idea was that a point of [the spectrum of the TAG theory of toric non-quasicoherent sheaves over a toric variety x] over a toric affine scheme y shuld be "a point p of x over y tw a toric open u of x to which p belongs" (?? ...) ... ??whereas at the moment i seem to be getting some sort of annoying parody of that instead ... ?? "point p of x over y tw a toric open u of _y_ to which p belongs" ... ???wait a minute, that doesn't seem to parse too well; it doesn't make sense (as far as i can see...) to say that a point belongs to a subspace of its domain of variation ... ???..... ????? ......

hmmm....

well, let me try to put that aside for the moment... even if it's more or less impossible to ... and say what i was going to say, anyway ...

which is... ?? maybe this at least fits with already more or less knowing that the category of direct limits of principal actions of a commutative monoid doesn't simply fall to pieces without its filtered colimits structure .... ????....

??and .... ??? imagining toric variety x over toric variety y ... ??as maybe exploding into pieces corresponding to toric opens of y rather than of x? ... ?? but there seemed to be problems with that even before noticing the non-parsing problem above...

??and ... ??? ??maybe contemplating all ways in which alleged presheaf (??or maybe pre-stack?) (??and also somewhat similar examples?? ... ??including non-toric analogs?? ...) in question is "bad" ... ???.... ??for one thing, to see how "bad" spectrums of _any_ (...) kind can get, let alone this kind ... ??? ... ?? having idly conjectured at various points that spectrums of even the most general TAG theories (or perhaps not quite so general ...) are somewhat good in certain ways ... ?? ...

?? maybe ... ?? not having enough (?? ...) models over multiplicative monoids of fields as a sort of "bad"-ness here ???? .....

?? had some idea about "non-separated" ... ???? ....

??? "morphism x : 1 -> 1, tw [??object u ... with multiplication and/or comultiplication operation??? ... ??? ... maybe epi-ness ... ??? ??? .... ??well, maybe all that i'm trying to say here is "coherently idempotent" ... ????... ??no wait... ?? "idempotent" commutative monoid ??] on which x becomes invertible" ?? .... ???? ....

??this as theory which really "wants" to have category-valued spectrum ??? ... ???...

?????? Z/n as idempotent commutative monoid in TAG environment _Z-set_ ?? .... ????? ......

??todd reminded me ... ?? universal property of day convolution over actual symmetric monoidal category x .... ?? ... "symmetric monoidal functor from x" ... ??affine vs non-affine case here .... ???? .....

???cartesian product of TAG theories .... ???? .... ??? ....

?? "explosion" ... ??? ....

????? ..... ???? ....