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1 vote
0 answers
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Homotopy limits indexed by a covering

We all know that the homotopy fiber of a continuous function $f: A \to B$ has a simple expression in terms of points and paths connecting them, that is $$ \textrm{hofib}_y(f) = \{ (x,\gamma) \in A \...
22 votes
3 answers
3k views

Necessity of hypercovers for sheaf condition for simplicial sheaves

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 ...