Exponential objects in a cartesian closed category: $a^1 \cong a$ Hi I'm having problems with coming up with a proof for this simple property of cartesian closed categories (CCC) and exponential objects, namely that  for any object $a$ in a CCC $C$ with an initial object $0$, $a$ is isomorphic to $a^1$ where $1$ is the terminal object of $C$. In most of the category theory books i've read this is usually left as an exercise, but for some reason I can't get a handle on it.  

For any object $x$, we have:
$$\operatorname{Hom}(x,a^1)\cong \operatorname{Hom}(x\times 1,a)\cong \operatorname{Hom}(x,a)$$
So Yoneda's lemma gives us that $a$ is isomorphic to $a^1$.
