Final object in fields of characteristic $ 0 $? In his answer to this question: Category of Field has no initial object, Arturo Madigin indicated that the field of rational numbers is the initial object in the category of fields of characteristic $ 0 $. 
(There is also an interesting discussion trying to characterize such fields here: Examples of fields of characteristic $ 0 $.)
Does the category of fields of characteristic $ 0 $ have a final object? Somehow it would be great if it were the real numbers, but because of my limited background, I can’t imagine showing either hom existence or uniqueness. 
Any ideas?

No. Any morphism between fields is injective, and there are fields of characteristic $0$ of arbitrarily large cardinality. 
