  It was recently proved by several authors that ribbon concordances induce
injective maps in knot Floer homology, Khovanov homology, and the Heegaard
Floer homology of the branched double cover. We give a simple proof of a
similar statement in a more general setting, which includes knot Floer
homology, Khovanov-Rozansky homologies, and all conic strong Khovanov-Floer
theories. This gives a philosophical answer to the question of which aspects of
a link TQFT make it injective under ribbon concordances.
