Acyclic fibration in the projective chain-complex model structure
= Acyclic fibration in the projective chain-complex model structure
{title2=$f_n\text{ surjective for all }n,\quad H_*(f)\text{ invertible}$}
= Projective acyclic fibration
{synonym}
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>.