Suppose that the category $\mathbb C$ is cartesian closed. How do I show that $C^T$ is isomorphic to $C$ for every object $C$, when $T$ is the terminal object?
I'm quite sure that I should solve the exercise rearranging the facts that $C\times T\cong C$ and that the functor $-^T$ preserves limits, being a right adjoint; still, I couldn't come up with any useful idea. I don't want you to solve it, I'd just like a small hint (since this seems an exercise that, once you had the right guess, becomes trivial). Thanks in advance