Exact sequence of sheaves
= Exact sequence of sheaves
An <exact sequence> of <sheaves of abelian groups> is a sequence of sheaf homomorphisms for which the image of each map equals the kernel of the next. Exactness can be checked on every <stalk of a sheaf>. Exactness of the associated sequences of sections on every open set is a stronger condition: a surjective sheaf homomorphism need only admit lifts locally.