Coherent analytic sheaf ($\mathcal{F}\text{ a coherent }{\mathcal{O}}_X\text{-module}$)

On a complex manifold, a sheaf of modules over the sheaf of holomorphic functions is coherent analytic if it is locally finitely generated and the kernel of every morphism ${\mathcal{O}}^r\to \mathcal{F}$ is locally finitely generated. The structure sheaf and locally free finite-rank sheaves are examples. Cartan theorem B gives vanishing of their higher sheaf cohomology on a Stein manifold.