On Tue, Apr 3, 2012 at 3:55 PM, Marshall Lochbaum <mwlochb...@gmail.com> wrote: > "The category of sets" is defined to be the category of sets and the > functions between them. It is an unambiguous term. If there is another > category whose elements are sets (i.e. the category of sets containing a > "base" element and the functions between them fixing that element), it will > be properly delineated.
Then this category must contain all possible arrows? > An arrow is only associated with one source and one destination. Thus there > is no arrow which leads from 0 to 0 and from 1 to 1. If we are in the > category of sets, this means each function has precisely one domain and > codomain. I think you are telling me that an arrow cannot represent an arbitrary function. Consider the function F(x) = x+1 F(1) = 2 F(2) = 3 There can be no arrow that leads from 1 to 2 which also leads from 2 to 3. We can have an arrow which leads from the set of all integers to the set of all integers, but that arrow cannot distinguish between the above function and any other function on integers. But this does not match what I read when I read about arrows/morphisms. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
