??so let x be a dimensional category, and then let x' be the dimensional category of x-objects equipped with actions by abelian group g ... ???or something?? ... ???what's this like??....

??is an x'-model maybe esentially an x-model together with a g-torsor?? ???or something?? ...??? ...

??maybe in some cases, but ... ???shouldn't it be a bit different from that, conceptually???....??? or aomething ?? ....

??well, so what about sort of same idea with ag theory or g theory, for example??

hmm... geometric theory case seems like it should be straightforward, no ?? ...???...

???something about ... ????a g-rep equipped with an action of h as a gXh-rep ... ???? ... ??or somethihng??? ...

??so consider ... ???the dimensional theory of "a t-model together with an a-torsor" where a is, for example, some finite abelian group ?? .... or something .... ???.....

???somethihg about ??"using gabriel-ulmer duality" (or something....) to simulate tneosr product via homming" ???? .... ???or something??? ... ???....