  We give a diagrammatic presentation of the category of
$\textbf{U}_q(\mathfrak{sl}_2)$-tilting modules $\mathfrak{T}$ for $q$ being a
root of unity and introduce a grading on $\mathfrak{T}$. This grading is a
"root of unity phenomenon" and might lead to new insights about link and
$3$-manifold invariants deduced from $\mathfrak{T}$. We also give a
diagrammatic category for the (graded) projective endofunctors on
$\mathfrak{T}$, indicate how our results could generalize and collect some
"well-known" facts to give a reasonably self-contained exposition.
