On Thu, 2009-02-05 at 20:52 -0600, Gregg Reynolds wrote:
I'm working on a radically different way of looking at IO. Before I post it and make a fool of myself, I'd appreciate a reality check on the following points:
a) Can IO be thought of as a category? I think the answer is yes.
No. At least not in any reasonable way.
b) If it is a category, what are its morphisms? I think the answer is: it has no morphisms. The morphisms available are natural transformations or functors, and thus not /in/ the category. Alternatively: we have no means of directly naming its values, so the only way we can operate on its values is to use morphisms from the outside (operating on construction expressions qua morphisms.)
N/A
c) All categories with no morphisms ("bereft categories"?) are isomorphic (to each other). I think yes.
No. "Discrete" categories which you seem to be talking about are isomorphic to sets (namely their set of objects). Not all sets are isomorphic.