Sunday, October 30, 2011

?? idea of ... smc as "generalized affine toric variety", then gluing such together along "open inclusions" corresponding to "localizations" ?? ....

(?? non-toric analog as well ?? ...)

?? to what extent do we understand why one-object smcs are unstacky here ??? .... ??? hmm, maybe we _do_ understand it pretty well ... ???? unit object as not really extra stuff ??? ... hmmm .... i'd been going to ask whether this was part of some "stabilization slope" that we should understand ... and i guess that that question still applies, but "unit object as not really extra stuff" seems pretty close to right track ... ??? ....

[?? disjunction] : [?? existential quantification] :: [?? pushouts and/or discrete sums] : [?? higher-dim colimits ... ??? coequalizers and/or co-invariants ... ??? ....] ??? ....... ??? existential quantification as sort of "decategorification" .... ??? .... ?? unstacky vs stacky (?? ...) version of "cover" / "covering" .... ??? ..... ???? .... ??? "no decent theory has existential quantification at outermost level" as less defensible than "no decent theory has disjunction at outermost level" ??? .... ??? ....

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