Acyclic fibration in the projective chain-complex model structure ($f_n\text{ surjective for all }n,H_{\ast }(f)\text{ invertible}$)

A map that is both a model fibration and a quasi-isomorphism. The homology isomorphism together with degree-one surjectivity forces surjectivity in degree zero. Equivalently it has the right lifting property against the generating cofibrations for nonnegative chain complexes.