For exercise 1.83,

Show that if \$$f:P\rightarrow Q \$$ has a a right adjoint \$$g\$$, then it is unique up to isomorphism. That means, for any other right adjoint \$$g'\$$, we have \$$g(q)\cong g'(q)\$$ for all \$$q \in Q\$$.

I'm having a little trouble getting started. I wanted to show that both \$$g(q) \geq g'(q)\$$ and \$$g'(q) \geq g(q)\$$, but I'm having trouble going from the definition of a right adjoint to this. Does anyone have any advice on how to get started?

Thank you!