[FOM] Axiom of Choice in Category Theory

[Laurent Delattre]

Hello,

I would like to discuss about the Axiom of Choice in
Category Theory.

If I am not mistaken, it is formulated the following
way:

"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".

Can someone explain why  D is required to be discrete?

Can F and G be seen as a pair of adjoint functors?

More generally, what is the relation between the Axiom
of Choice and adjunction?

Thanks,

Laurent



	

	
		
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