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  "body": "\n## Summary\n\nThe nerve of a cover of a space is the [[simplicial complex|V8GZ0W1ZZ5]] that records which members of the cover meet.\nIt has one vertex for each nonempty member, and a set of members spans a simplex when they have a common point.\nBy the nerve theorem, a good cover has a nerve with the same homotopy type as the space.\nThis turns topology into combinatorics, and nerves are also the basis of Čech cohomology.\n\n## Explanations\n\n### L1 human\n\nCover a space with overlapping patches.\nDraw a dot for each patch, an edge between two dots when the patches overlap, a triangle when three patches share a point, and so on.\nThe resulting shape is the nerve.\nCover a circle by three arcs, each overlapping the next, with no point in all three.\nThe nerve is the boundary of a triangle, which is again a circle.\n",
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