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Show that if \(f: P \to Q\) has a right adjoint \(g\), then it is unique up to isomorphism. That means, for any other right adjoint \(g'\), we have \(g(q)\) isomorphic to \(g'(q)\) for all \(q \in Q\).
Is the same true for left adjoints? That is, if \(h: P \to Q\) has a left adjoint, is it necessarily unique?