?? "extension of AG theory of g-torsor" .... ?? which we're trying to construe as "g-rep-enriched AG theory" ... ?? ....

?? underlying just plain AG theory being .... ?? usual de-enrichment ??? .... ?? namely taking invariants subspace ... ??? ....


?? then also equipping model with frame of its underlying g-torsor ... ??? .... syntactic weak coproduct with g-rep-enriched theory of ... "a frame". i guess .... ??? which is what, syntactically ??? .... ??well, i guess that it is after all just something like ... "introducing the non-invariant elements in the enriched hom spaces as new morphisms" ... ?? "after all" because i had some vague guesses along those lines ... which, because of the way in which the new morphisms give rise as well to new objects via coequalizers ... leads me to think about ... ??? annoying / intriguing "locally internal category" appendix in baby elephant, and ideas connected in some way (in my mind ...) with that .... ????.... snow-globe / potemkin model ...

??? alternative (perhaps lax?) de-enrichment process here ??? ..... adjoint ... ??? .... "total vs fiber" ?? ... ?? .... not "preserving cocompleteness" ?? ... ???? .....

??? still bugged by level slip here ????? ..... ???? g acting on theory t, vs on t-model .... ??? and/or both, with "riding" ?? .... ??? "slipping/sliding along long exact homotopy sequence" ... ??? ...

?? simply "g-torsor (bundle/object)" after all ?? .... ??? .... x # [??cayley picture of g-torsor] -> y as "new/generalized,non-invariant morphism" .... ????? simply kleisli category ????? ...... ???? kleisli category and this "locally internal" / "snow-globe" / "potemkin" stuff ?????? ...... ?? kleisli, (and /) or co-kleisli ?? ... ??? ... ?? adjoining coequalizers of new morphisms sounds like kleisli rather than co-kleisli ??? ... i mean .... ??? .... ??? co-/kleisli vs co-/eilenberg-moore .... ??? ....

???? work out example of .... gl(1) acting on affine line .... ????? ....

k[x]-module ...

??? hmmm, maybe there really was a kleisli/co-kleisli duality flip just above, combined in some way with a long exact sequence level slip .... ??? "old vs new" confusion .... ??? affine line doesn't have interesting bundle of gl(1)-torsors, but orbit stack of tautological action of gl(1) on it does .... ???? ..... ???? ....

!! work this out !! ..... ??? ....

??? typical (?? ...) vector space with linear operator as ... ??? not turnable-into graded module of k[x]x .... ???

..... ???? .... ..... ???? .....