The Stacks project

Definition 6.8.1. Let $X$ be a topological space.

1. An abelian sheaf on $X$ or sheaf of abelian groups on $X$ is an abelian presheaf on $X$ such that the underlying presheaf of sets is a sheaf.

2. The category of sheaves of abelian groups is denoted $\textit{Ab}(X)$.