??so maybe part of todd's point was to consider the "fixed point category" of a geometric morphism ... ??so what _is_ this like ??

todd points out that lots of nice monads on the category of sets have no fixed point objects ...

??so let x be a small-ly cocomplete category and x1 an object in x; then consider the "globalization/localization adjunction" arising from this; thus globalization assigns to a set s the object given as the s-fold sum of copies of x1, and localization assigns to an object x2 the set [x1,x2] ... ??then consider the "fixed point objects" here ...

??for example x = _set_^op and x1 = 1 ... ??? ... ???...

??hmmm... ??or what about x1=2 ??.... ??relationship to "single classical universe model theory" ?? ... and so forth ... ??...

??something about poset-enrichment here ?? ... and so forth ... ??...

??something about ... other ideas besides "fixed point objects" idea here ... ???....

??idea that term "localization" here _is_ weird because suggests idea of... ??restriction process opposite (or something ... ?????? ...) to kan extension ... ??... i mean "opposite to" in other way, i guess ???... ????... ??is this related to the usual confusion about in what sense "kan extension" "extends" ??? ... ???...