Stalk

Summary

The stalk of a sheaf at a point is the set of germs of sections at that point. A germ is a section defined near the point, where two sections are identified when they agree on some smaller neighbourhood. Stalks capture the local behaviour of a sheaf at a single point. Many properties of sheaves and of maps between them, such as being zero, injective or surjective, can be checked stalk by stalk.