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  "body": "\n## Summary\n\nCellular homology is a homology theory for [[CW complexes|5W95QFHXPR]] whose chain groups are free abelian groups on the cells.\nIts boundary maps are built from the degrees of the attaching maps of the cells.\nIt agrees with [[singular homology|M0Q5CFJ7ZH]], so it is often the fastest way to compute the singular homology of a space with a cell structure.\n\n## Explanations\n\n### L1 human\n\nA CW complex is built by gluing points, then intervals, then discs, and so on.\nCellular homology counts these building blocks in each dimension and records how the boundary of each cell wraps around the cells one dimension lower.\nThe sphere $S^2$ can be built from one point and one disc whose whole boundary is collapsed to the point.\nThere is one cell in dimension $0$, one in dimension $2$, and no boundary map can be nonzero.\nSo the homology is $\\Z$ in dimensions $0$ and $2$ and zero elsewhere.\n",
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