Bounded below derived category of sheaves
= Bounded below derived category of sheaves
{title2=$D^+(X)$}
The category $D^+(X)$ is obtained from bounded below <cochain complexes> of <sheaves> by passing to cochain-homotopy classes of maps and then inverting <quasi-isomorphisms>. It can equally be modeled by injective resolutions. The cohomology-sheaf functors descend to this localization, and an object is zero exactly when all its <cohomology sheaves> vanish.