fan as spectrum over additive monoid of positives ?? .... ???? ?? todd's subtlety ?? ... ???? .....

??? conical wrapping up of toric variety, after all ???? .... ???? .... accidental topos ... ??? ...

?? spectrum over multiplicative monoid of unitaries ??? ....

"galois" action of gl(1,r) on add(r)-spectrum of toric variety ...... ???

torus stackiness .... ?????

kaleidoscopic toric variety ..... ???? weylotope ... ??? generalize to arbitrary toric variety ???

?? pos vs neg, vs >=1 vs <=1 .... ???? ..... ?? some confusion ???....

?? toric schubert variety .... ???? .... ??? some confusion ??? .... bruhat cell ... affine space ... zariski closure .... non-singular toric variety ... ??? .....