Let $F: \mathscr{C}\to \mathscr{C}^{op}$, with  an adjoint $G$, and   $\eta: 1_\mathscr{C} \Rightarrow G\circ F  $ and $\varepsilon: F\circ G\Rightarrow 1_{\mathscr{C}^{op}}$ with components (in $\mathscr{C}$):

$\eta_M: M\to G(F(M))$ and $\varepsilon^{op}_N: N\to F(G(N))$ such that the compositions (in $\mathscr{C}$):

$F(M) \xrightarrow{\varepsilon^{op}_{F(M)}} FGF(M) \xrightarrow{F^{op}(\eta_M)}F(M)$ and

$G(N) \xrightarrow{\eta_{G(N)}}GFG(N) \xrightarrow{G(\varepsilon_N)}G(N)\ $ are units.

Moreover suppose   $G=F^{op}$ and $\eta$ a isomorphis transformation.
Follow that  $F$ is  full, faithfull and reflect isomorphisms (consider $F(f)\circ \eta_M=\eta_{M'}\circ f$ for $f: M\to M'$), then also  $G=F^{op}$ reflect isomorphisms, from above: $\varepsilon$ is Iso.
Observe that the components of $\eta: 1_\mathscr{C} \Rightarrow F^{op}\circ F  $ and $\varepsilon^{op}:  1_{\mathscr{C}}\Rightarrow F^{op}\circ F$ are of type: $\eta_M: M\to F\circ F(M)$ and  $\varepsilon^{op}_M: M\to F\circ F(M)$.

Question: Is true that  $\eta =\varepsilon^{op}$ ?


Question: Are questions regarding System76 hardware allowed?
Answer: As Jorge mentioned, it would be dependent on what the questions actually relate to.

Hardware related questions are better suited for one of the other sites.  Hardware compatibility as well.

Asking "How do I upgrade the BIOS?" is one of those edge-case questions, it could be on topic, it could be offtopic.  If you specify that you're wanting to update the BIOS via Ubuntu, then it becomes a non-edge-case question and is valid for here.