subdivision, stackiness, poisson blow-up ... ?????.....

??? "subdivision" ... "blow-up" .... "explosion" ... ???? ....

??? comparison between two ideas about "toric morphism" ... 1 : comm monoid hom and / or TAG theory morphism ... ??? .... vs 2 : "torue-equivariant map riding torus morphism" ... ??? trying to compare in detail ... ?? nice simple examples ?? ....

???functor from _comm monoid_ to _dimensional algebra_, assigning to commutative monoid x the dimensional algebra [monoid-alg(x) graded by fraction-group(x)] ... ????

?? extending this in nice way to functor from _TAG theory_ to _AG theory_ ??? .... ???? ..... ??? extra objects, corresponding to .... ??? .... fraction-group of "center" ??? .... ???? ..... ???? .....

?? comparison to leaving out the grading ... ???

?? toric (?? ...) aspect of "blowing up "comm alg" sub-stack (?? ...) of "assoc alg" stack" ... ???? .... ??????????????? ..... poisson alg .... ???????...... ??? level slips and strange loops ... ???? .....

????level slips and strange loops ??????????? .......

?? dim 1 face (?? "ray" ??) of cone dual to cod 1 face of cocone ... ??? visualization ... ???... ?? "nail down the points on the cod 1 face; in fact mod out by them, and map the residual ray to the standard ray ..." ???

?? dim 2 face of cone dual to cod 2 face of cocone ... ??? visualization ... ??
?? "nail down the points on the cod 2 face; in fact mod out by them, and map the residual dim 2 "silhouette" (?? ...) wedge to the standard ray ..." ??? ....

?? cocone co-face _not_ as just "omitting corresponding cocone face" ... ?? do we really still believe that cocone co-face has corresponding cocone face ??? ... ?? well, maybe yes ... ??? ..... ?? some confusion ... ???....

?? can't just take an extreme ray of a cone and then take the convex hull of the other extreme rays ..." ... ??? at least, not without ... ??? expecting silly things to happen ?? ... ???? .....