Wednesday, March 23, 2011

??so what _about_ doctrine of symmetric monoidal filteredly cocomplete (??k-linear ... or omit this for the toric case ... ??? ...) categories ??? ... and so forth ...

??what about something about... ??given an ag theory, taking the theory of this new doctrine given by something about ... ??just the stuff generated from the unit object by filtered colimits, or something ??? ... ???is this part of an adjunction / interpretation of doctrines ??? ... ???... and so forth ... ???

???something about ... ???stuff here about ... "local vs twisted" ... ??and so forth ... something about relationship to doctrine of dimensional theories ... and so forth ... ???...

??what _about_ something about ... ??relationship between colimits of formulas and ... ???(weak ... ??...) geometric colimits of theories?? ... ?? ... or something ... ??perhaps sort of showing up here... or something ... ??...

??still confused by "change of doctrine", as for example here ???...

??found myself saying something about "same moduli space, but with more / less structure" (... or something....) ... ??but then tried refining it to "same moduli stack ..." ... ???which apparently just made things worse?? ??or something ... ???but then tried "same model groupoid ...", which might be helping ...

??so maybe it was just a big old level slip that was bugging us ... (categorfied ... ??...) structure on a model groupoid, vs (not categorified ...) structure concept inherent in given groupoid ... ??? ??or something ...

??so what _about case where it's not just same model groupoid, but same model category ... ??and so forth ... ??...

??so what _about_ trying to understadn lots of examples of extra structure on model groupoids here ... toric ... dimensional ... ??something about this "filteredly cocomplete ..." stuff ... and so forth ... ??? ....

??so what about something about ... postnikov-like factorization (and so forth...) of certain (2,1)-fmnctors here ?? ... and so forth ...

??so what _about_ projective n-space as theory of doctrine of symmetric monoidal filteredly cocomplete categories?? ??or something .... ??hmm, so what about something about "intended environment" here ?? ... and so forth .... ???...

??confusion??? ???something about ... ??maybe unit object is _missing_ here ??? .... ???or something ??? .... ???.... ??something about "semi-monoidal ..." ... ?? ... ??...

???relationship to something about ... ??unit object being non-projective?? ... ??or _something_ ?? ???what about "projective : presheaf :: ?? : filteredly cocontinuous presheaf" here ?? ... or something ... ??? .... hmmmm .... ????.... ??what _about_ relationship to "flat", or _something_ ???? .... and so forth .... ????

???hmm, what _about_ still model/formula confusion here ??? ... something about diaconescu's theorem and flat _co_-presheaf here ??? ... and so forth ... ???...

??what _about_ something about ... ??finite top space ... ??something about "minimal neighborhood of a point" ... and so forth ... something about variance confusion ... vs closure of a point ... ??...

???something about ... ??model/formula confusion and something about ... ??torsor of commutative monoid ... ???and something about tensor product of such things ... ???and so forth ... ???.....

No comments:

Post a Comment