[FOM] Axiom of Choice in Category Theory
Laurent Delattre
nouvid-fom at yahoo.fr
Wed Feb 1 22:40:10 EST 2006
Thank you for the numerous replies to my questions.
Now I understand well why D should be discrete.
However, saying that a (small) category is discrete
amount to say it is a set. Thus the following
statement of the Axiom of Choice in Category Theory
has a set-theoretic flavour:
"Let C and D be (small) categories such that C is not
empty and D is discrete. Let F be a functor from C to
D. There exists a functor G from D to C such that
FGF=F".
Are there more "categorical" ways to state this axiom?
I was hoping that it might be expressed by some
adjunction but it appears it is not possible.
Laurent
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