A transcendental approach to Koll\'ar's injectivity theorem II

We treat a relative version of the main theorem in my previous paper: A transcendental approach to Koll'ar’s injectivity theorem. More explicitly, we give a curvature condition that implies Koll'ar type cohomology injectivity theorems in the relative setting. To carry out this generalization, we use the Ohsawa-Takegoshi twisted version of Nakano’s identity.