  We treat Koll\'ar's injectivity theorem from the analytic (or differential
geometric) viewpoint. More precisely, we give a curvature condition which
implies Koll\'ar type cohomology injectivity theorems. Our main theorem is
formulated for a compact K\"ahler manifold, but the proof uses the space of
harmonic forms on a Zariski open set with a suitable complete K\"ahler metric.
We need neither covering tricks, desingularizations, nor Leray's spectral
sequence.
