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  "body": "\n## Summary\n\nSheaf cohomology assigns groups $H^q(X, F)$ to a topological space $X$ and a sheaf $F$ of abelian groups on $X$.\nThey are the right derived functors of the global sections functor.\nIt measures the failure of local sections to glue into global sections.\nWith a constant sheaf it recovers ordinary cohomology on reasonable spaces, and with other sheaves it gives local coefficients, Borel–Moore theory and Poincaré–Verdier duality.\nThe general notion is sheaf cohomology in algebraic geometry and topology.\n\n## Explanations\n\n### L1 human\n\nA sheaf is a rule that tells you what the allowed local data are on each open piece of a space, such as continuous functions or locally constant functions.\nOften local data agree on overlaps but still do not come from one global object.\nSheaf cohomology counts such obstructions.\nFor example, on the unit circle in $\\C$, a continuous square root of $z$ can be chosen on each small arc.\nBut these choices cannot be made to fit together around the whole circle.\nThis obstruction is a nonzero class in $H^1$ of the circle with coefficients in $\\Z/2$.\n",
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