?? accidental infinity-topos of toric p^1 ... ?? ....

?? given "topological dynamical system", consider ... ??? space of "weak z-histories" ... ??? ....

?? vague "quantum measurement" feeling here ?? ...

?? idea of derived category (and / or "weak"-er version ... ?? ...) as about "unification of limits and colimits" .... ??? problematicness of "unstable analog" here ??? .... ??? ....

?? infinity-geometric morphisms between accidental infinity-toposes ... ??? ....

?? "pair of topological dynamical systems ew z-anti-equivalence between their weak z-history spaces" ... ??? ...