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!

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!