Ribbon homology cobordisms and link Floer homology

We make use of link Floer homology to study cobordisms between links embedded in 4-dimensional ribbon homology cobordisms. Combining results of Daemi--Lidman--Vela-Vick--Wong and Zemke, we show that ribbon homology concordances induce split injections on H\!F\! L⁻. We also make use of the torsion submodule of HFL⁻ to give restrictions on the number of critical points in ribbon homology concordances.