Solution
= Solution
Apply the inverse transpose formula to $\eta_A$, which by definition is the transpose of $1_{FA}$. This gives $\varepsilon_{FA}F\eta_A=1_{FA}$. Likewise $\varepsilon_B$ transposes to $1_{GB}$, so $G\varepsilon_B\eta_{GB}=1_{GB}$. Hence the <triangle identities for an adjunction> are
$$
\boxed{\varepsilon_FF\eta=1_F,\qquad G\varepsilon\eta_G=1_G.}
$$
These are equalities of <natural transformations>; their components are exactly the two identities just proved.