Sunday, October 9, 2011

?? passage from comm ring to ag theory via taking module ag theory ... ??? as doctrine morphism, or as not ... ??? .....

?? globalization/spectrum adjunction here .... ??? hmmm, i was really expecting this _not_ to be a doctrine morphsm, but maybe it really is ..... ???? "underlying propositional theory of predicate theory" ??????? ....... ?????? .......... ?????????? ..........

?? wait, maybe (??...) some confusion here .... "spectrum" as not landing in _comm ring_ ???? .....

(i think part of what i was originally going to suggest here is that if this wasn't/isn't a doctrine morphism then maybe whatever we do with it might be interesting to try with other non-[doctrine morphism]s ... ?? but maybe also now, if it _is_ a doctrine morphism, interesting to try whatever we do with it to other doctrine morphisms .... ???? ..... ???? "change of colimits" .... ????? .....)

??? colimit vs 2-colimit here ??? ....

_comm ring_ -> _comm ring formal (2,1)-colimit_ -> _ag theory_

???? right adjoints to both of those ??? ..... ??? and to composite ??? ...

??? confusion ??? ....

??? fe ..... ???? consider poorer doctrine = dimensional, richer = ag .... ???? "dimensional spectrum of ag theory" ....... .... ??? .... globalization ..... ???? ..... ... ??? ....

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