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I'm trying to understand where the definition of simplicial sheaf on a space/site comes from. For a presheaf $F$ of sets on a topological space $X$, the sheaf condition can be viewed as saying that ...

Let A be an abelian category, and X a topological space. There are two ways one could try to construct some oo-category of sheaves on X from this data: Consider the category $Sh(X,A)$ of sheaves on ...

Suppose $U'\cup U''=X$ is an open cover $U$ of a topological space $X$ and $F$ is a sheaf on $X$ with values in abelian groups. There is a special instance of the Grothendieck spectral sequence ...