  We provide a detailed derivation of the mode-coupling equations for a
colloidal liquid confined by two parallel smooth walls. We introduce
irreducible memory kernels for the different relaxation channels thereby
extending the projection operator technique to colloidal liquids in slit
geometry. Investigating both the collective dynamics as well as the
tagged-particle motion, we prove that the mode-coupling functional assumes the
same form as in the Newtonian case corroborating the universality of the
glass-transition singularity with respect to the microscopic dynamics.
