Friday, May 27, 2011

?? "relatively free cocompletion of cocomplete category x, relative to existing colimits, as x itself ..." .... ???but ... ???question of totality here ???? .... ????? .....

???once again confused between "small-valued" and "small-ly presented" ... ??? ???latter has better chance of implying former than vice versa ... ?????....

???? "how total is total" ??? ..... ?????.....

???maybe for total categories, small-valued really does imply small-ly presented ???? .....

???todd also said something about .... ??? between total categories, cocontinuous functors have right adjoints ???? ..... ???again making me wonder about relationship to locally presentable ... ??? ....

todd's "epistemology" paradise-dream as .... ??? (??in part?? ...) allowing simultaneous totality and co-totality ??? .... which according to silly analogy i was trying to make seems like ... ??? "reducing quantum world to classical world" ??? .....

??idea of ... some kind of table ... cardinality parameters for ... ??size of diagram scheme ??? .... ???size of target category ... ?? size of values ... ??? .... ??? showing relationships between / constraints on ... ??? ..... resulting categories of formal colimits .... ??? .... ??? .....

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