When reading about Cartan's theorems for Stein manifolds (theorems A & B), about half of the sources state this in terms of coherent sheaves and half of them uses coherent "analytic" sheaves. I was wondering why some sources deem it necessary to introduce the adjective "analytic"?
As far as I know all complex manifolds are complex analytic spaces and, hence, the coherent sheaves associated to their structure sheaves are automatically analytic.