?? double-speed dynamical system ... ??? ... ?? "n-fold acceleration" ... ??? ....

?? "half-speed" ... ??? left vs right adjoint ... ??? ....

?? "history" ... ???? ....

?? adjoint pair of bimodules ... ?? essential geometric morphism .... ??? .....

?? adjoint bimodule and absolute weight(-ed colimit) ??? ..... ??? ....

??? absolute weight and essential geometric morphism ??? .... ???? "cauchy completion" .... ???? ..... "morita/karoubi saturation" .... ???? .....

?? "essential geometric morphism as means of reconstructing (?? as best possible ?? ...) functors between sites ...." ... ??? then "ghost" / "virtual" functors .... ??? ....

??? but .... ???? all those adjoint bimodules coming from actual functors ..... ???? .... what sort of alleged "absolute weights" do these correspond to ???? .... ???? .... ??? variable absolute weights ??? ..... ?? plain module (with adjoint ... ???) as "constant" case .... ??? ..... so adjoint module as "virtual object" of site ??? ..... ??? ... ??? seems to fit ??? .... ????? ......

?? maybe also fit with speculation we had about "accidental infinity-topos" and geometric morphism involving such ??? .... ????? ..... ???? .... ??? essential ... ??? .... ???? .... ???? not sure .... ??? .... ???? ....

??? "absolute" .... "stable" .... ???? ....

??? stable paradise .... ????? lots of virtual objects ??? .... ???? .... ????? ..... ?? try to straighten this out ... ??? ... ??? "derived-level cauchy completion of single-object enriched category as including "all" of its modules" .... ?????? ...... ?????? ..... ??? "karoubi ..." .... projectives ..... ???? .... ???? .... ???? .... "projectiveness as vacuous at derived level" ...... ???? ..... ???? ..... ?? familiar ??? .... ???? ... ???? .....

?? "morita-equivalence" .... "morita-map/functor" ... ?? adjoint bi-module ... ???? .... essential geometric morphism ..... ???? .......

?? "ambijunction" ... ???? .... ....... ??????? .......

?? "cartesian bicategory" .... ???? ....