Sheaf of abelian groups
= Sheaf of abelian groups
= Sheaves of abelian groups
{synonym}
A sheaf of abelian groups is a <sheaf of sets> whose sections on each open set form an <abelian group> and whose restriction maps are group homomorphisms. Its <stalk of a sheaf> is the corresponding group of germs. Kernels are computed on sections, whereas cokernels are obtained by <sheafification> of the sectionwise cokernel. An <exact sequence> can therefore be checked on stalks.