We connect the Khalkhali-Pourkia and Bartulovic approach to Hopf-cyclic coefficents in the braided setting to the Laugwitz relative center construction. The extra ingredient is the ``stacking" product on $HH(\mathcal{B})$, the Hochschild homology category of the braided category $\mathcal{B}$. The differences between the center and anti-center situations force a choice of a twist on $\mathcal{B}$. The choice matters, leaving it open to interpretation.