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 $\textit{Ab}(X)$.

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View Definition 6.8.1 as pdf