Tuesday, March 22, 2011

??something about "toric voodoo"... ???something about "generic point of toric (sub-)variety ... ??or something ... and so forth ...

??bunch of ideas about filtered colimits ....

???is this a "tame" (??something about "small" ... ??...) monad on _cat_ ?? or something??? ... and so forth ...

?? weak colimits of categories with filtered colimits .... ??as related to weak colimits of toric schemes / stacks or something??? ... and so forth ...

??also something about geometric filtered colimits of geometric theories and of tag theories...


??also algebroid / "ordinary" case ??? ... or something.... and so forth... ...something about ag theories ... ??...


???something about ... eckmann-hilton... ??stretched in some peculiar way ???? or something???

??any variance confusion here ???? .... ???or something ??? .... hmmmm .... commutative monoid .... ????.... ...hmmmm.... ????....

???something about "accidental" vs "deliberate" here??? .. and so forth ... ???danger that accidental works better than deliberate here ?? ... ??or something ?? ...

??symm mon cat with filtered colimits... and so forth ... ??something about modules and graded modules and so forth here .... ??? ...

??something about... "free filteredly cocomplete" =?= "affine" ????? or something???.... and so forth... ????.....

??something about gabriel-ulmer duality ... ??some sort of "strange loop" here, maybe?? ... something about filtered colimits ... as involved in foundations of gabriel-ulmer duality ... (??or maybe just some special case or something???...) ... ???but then also something about ... model category of topos ... ??... tending not to have too many other colimits ... ??or something ??? ... and so forth ... ??...

??every groupoid has all filtered colimits ?? ...

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