Ghost morphism in a derived category
= Ghost morphism in a derived category
A ghost is a morphism inducing zero on every <cohomology sheaf>, but it need not itself be zero. For the equator $j:S^1\hookrightarrow S^2$ and complement $i:U\hookrightarrow S^2$, the connecting morphism $j_*\mathbb Q_{S^1}\to i_!\mathbb Q_U[1]$ is a ghost. Its source and target have <cohomology sheaves> in different degrees, but its induced map $H^1(S^1)\to H_c^2(U)$ is nonzero, proving that the derived morphism is nonzero.