?? orbit closure wrt t-action on g/b .... ?? choosing which t vs choosing which orbit ... ???? ....

?? actually choose not just orbit, but basepoint for it .... ???? ....

?? apartment-flag configurations .... ?? bit about shortage of "infinitesimal double cosets" above continuity/wildness threshold ?? ...

?? a1 kaleidoscope toric variety .... projective line .... apartment-flag orientations ... ???? hmm, still below continuity threshold ?? ... ?? cross-ratio still needs another point to kick in ... ???.....


?? generalized morphisms of toric varieties ... ?? kleisli morphisms for monad "direct sum with (k,mult)" ??? .... ?? geometric interpretation via inclusion into monad "monoid k-algebra" .... ??? amounting to "allowing translations" ????? .....

?? does sort of fit with certain past ideas about ... ?? using something like this (...) to unify "x=0" flavor ideals with "x=y" flavor .... ???....

?? possibility of u(1,k) instead of (k,mult) here ??? ....

??? but what about generalizing not just the morphisms but the objects too ?? ... not just kleisli category but eilenberg-moore category .... ?? ...

?? twisted monoid algebras for (?? how exhaustive ??) example ???

?? subvarieties of affine / projective plane ... ??? .....

??? nilpotence ... ??? ....

(?? progression eilenberg-moore / object, kleisli / morphism, ... ??? .... ??? ....)

?? generalized fans here ??? ..... ?? maybe similar to what we already sort of worked out with monad "direct sum with affine coordinate ring of affine toric variety" ?? .... ??? .... ??? some added trickiness / interestingness ??? ....

???? "flatness" issue here ????? ......

?? how this all relates to accidental topos theory ??? .... ??? complications with zero / pointedness ??? ....

?? test this "allowing translations" idea on torus .... ???? not at all clear to me yet whether it's correct .... ???? ....