  We associate to each Temperley-Lieb-Jones C*-tensor category
$\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ with parameter $\delta$ in the
discrete range $\{2\cos(\pi/(k+2))\,:\,k=1,2,\ldots\}\cup\{2\}$ a certain
C*-algebra $\mathcal{B}$ of compact operators. We use the unitary braiding on
$\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ to equip the category
$\mathrm{Mod}_{\mathcal{B}}$ of (right) Hilbert $\mathcal{B}$-modules with the
structure of a braided C*-tensor category. We show that
$\mathcal{T}\!\mathcal{L}\mathcal{J}(\delta)$ is equivalent, as a braided
C*-tensor category, to the full subcategory $\mathrm{Mod}_{\mathcal{B}}^f$ of
$\mathrm{Mod}_{\mathcal{B}}$ whose objects are those modules which admit a
finite orthonormal basis. Finally, we indicate how these considerations
generalize to arbitrary finitely generated rigid braided C*-tensor categories.
