Thursday, March 17, 2011

??so what about something about ... ??good definition of "quasicoherent sheaf" via kan extension (and so forth...), vs conventional annoying definition ... ???trying to systematize / generalize this ??? ... ??systematic way of interpreting object in value of (??(2,1)- ??...) kan extension (or something...) as "sheaf" in some way ... ??? and so forth ...

??something about version of adjunction between [_pre-stack(_comm ring_)_ ??... or something...] and _ag theory_ using categories instead of groupoids ?? ... (2,2)-adjunction instead of (2,1)-, or something ???...

??so what _about_ "fixed points" (or something ...) of various adjunctions and/or "galois connections" here ??? ... something about including toric case ... and so forth ...

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