  Kashaev and Reshetikhin previously described a way to define holonomy
invariants of knots using quantum $\mathfrak{sl}_2$ at a root of unity. These
are generalized quantum invariants depend both on a knot $K$ and a
representation of the fundamental group of its complement into
$\mathrm{SL}_2(\mathbb{C})$; equivalently, we can think of $\mathrm{KR}(K)$ as
associating to each knot a function on (a slight generalization of) its
character variety. In this paper we clarify some details of their construction.
In particular, we show that for $K$ a hyperbolic knot $\mathrm{KaRe}(K)$ can be
viewed as a function on the geometric component of the $A$-polynomial curve of
$K$. We compute some examples at a third root of unity.
