The Universal Coefficients Theorem states that
$0\rightarrow H_n(X)\otimes G\rightarrow H_n(X;G)\rightarrow\operatorname{Tor}(H_{n-1}(X),G)\rightarrow 0$
splits, but not naturally. In all the algebraic topology contexts I've come across, "natural" implies commutativity, but I don't see what a "natural split" means. Can someone give me an explicit definition?
Edit:
From what I've read... if I understand this correctly, splitting naturally implies that if
$0\rightarrow A\rightarrow A\oplus C\rightarrow C\rightarrow 0$
and
$0\rightarrow A'\rightarrow A'\oplus C'\rightarrow C'\rightarrow 0$
and given maps $a:A\rightarrow A'$ and $c:C\rightarrow C'$, the map $A\oplus C\rightarrow A'\oplus C'$ has to be the map $(a,c)$ in order for the diagram to commute.