A natural transformation $\alpha \colon F\Longrightarrow G$ is a natural isomorphism if there exists a natural transformation $\alpha ^{-1}\colon G\Longrightarrow F$ such that
\begin{align*} \alpha ^{-1}\circ \alpha =\text{id}_{F},\\ \alpha \circ \alpha ^{-1}=\text{id}_{G}. \end{align*}
