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\begin{proof}
Suppose that $\eta_{A}$ is an isomorphism for every $A\in\cC$, where
$\eta_{A}\colon F(A)\to G(A)$ is the morphism of the natural transformation
- coresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
+ corresponding to $A$. Then $\eta^{-1}$ is simply given by the morphisms
$\eta^{-1}_A$.
Now assume that $\eta$ is an isomorphism, i.e. $\eta^{-1}\circ\eta = \id_F$.