?? whether for example spec(k[x,y]/y^2=x^3) should (...) be (...) a toric variety according to conventional "torus action ..." philosophy ... ???? ....

?? toric variety weakly modded out by some part of its own torus ... ??? accidental topos thereof ...????.....

?? also case where accidental topos is sequences of sets, or of objects from simpler accidental topos ... ??? ....

??? f : N^d -> Z ... ???? where ... image of f perhaps "doesn't cleanly split off" ??? .... ?? anything like this ??? .....

??? .....