Let $F:\mathscr A\to \mathscr B$ be a left adjoint to $G:\mathscr B\to\mathscr A$. Write overline $(\overline {\circ})$ for the (either direction) of the bijection $$\mathscr B(F(A),B)\simeq \mathscr B(A,G(B))$$ It's known that $\overline{g:F(A)\to B}=G(g)\circ \eta_A$ and $\overline {f:A\to G(B)}=\epsilon_B\circ F(f)$, where $\eta$ and $\epsilon$ are the unit and counit of the adjunction.
These equalities are easy to prove (by applying the naturality in $A$ and $B$ to the arrows $g$ or $f$), but I'm having a hard time memorizing them (and proving them all the time I need them is not very practical). Is there an easy way to memorize these equalities? Are there any mnemonics maybe?