?? point/path ambiguity in interpretation of fan ... ?? already worked some of this out, but ... ??? should be some very nice clear picture(s ?? ...) .... ???? ....

?? s^1 spectrum of toric variety ???? .... ??? to what extent _did_ we (explicitly or implicitly ...) work this out ?? ...

?? arbitrary sym mon cocontinuous fr between accidental toposes ... ???? "localize and reassemble" ... ???? try to prove that / check whether this shows arbitrary such fr is "good" ... ??? ...

?? try to exploit further idea of ... ??? developing concepts like "good embedding of dualizable objects" in terms of walking examples .... ??? ....

?? tqs(p^1) .... as sym mon cocomplete cat ... ??? epi from 1+1 to invertible object x with mere _property_ ??? ... ??? .... confusion ... ??? filtered vs graded .... ???? dual object as extra stuff .... ???? .... ?? i guess that part of the point is supposed to be that you don't _need_ any extra stuff but that conjecturally it's convenient to use dual object as such stuff anyway ... then bind it tighter (somehow ... ??? ...) so the extraness goes away .... ??? ...