  We consider the question of unicity of types on maximal compact subgroups for
supercuspidal representations of $\mathbf{SL}_2$ over a nonarchimedean local
field of odd residual characteristic. We introduce the notion of an archetype
as the $\mathbf{SL}_2$-conjugacy class of a typical representation of a maximal
compact subgroup, and go on to show that any archetype in $\mathbf{SL}_2$ is
restricted from one in $\mathbf{GL}_2$. From this it follows that any archetype
must be induced from a Bushnell--Kutzko type. Given a supercuspidal
representation $\pi$, we give an additional explicit description of the number
of archetypes admitted by $\pi$ in terms of its ramification. We also describe
a relationship between archetypes for $\mathbf{GL}_2$ and $\mathbf{SL}_2$ in
terms of $L$-packets, and deduce an inertial Langlands correspondence for
$\mathbf{SL}_2$.
