Sunday, April 15, 2012

?? bit about ... exposure to striking examples of left universal properties of algebraically structured categories, then realizing that much simpler (?? but as a whole also ultimately striking in their own way ... ?? ...) but somewhat analogous examples form secret subtext of alg geom ... ?? is "simpler" really right idea here ?? ... ??? maybe "tradeoff" ??? .... those original (...) striking examples that i was exposed to tended to be "rich at doctrine level but poor at theory level" ... ?? some other examples vice versa .... "poor" not really pejorative here; very "poor" doctrine as allowing its theories to be interpreted in great generality .... ??? .... ?? and somehow encouraging (??? ...) development of great variety of theories, some complicated .... products doctrine, limits doctrine, limits and colimits doctrine .... ??? .... (?? not to overdo it though ... ??? ... greater expressiveness of limits plus colimits over just limits, for example, as ... ?? also somehow encouraging development .... ??? .... ???? ....)

?? so maybe idea should be to mention both some "rich doctrine poor theory" and some "poor doctrine rich theory" examples (?? explicitly noting ocntrast to some extent ?? ....) as prelude to ag situation ..... ???? .....

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