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  "body": "\n## Summary\n\nThe mapping cylinder of a continuous map $f \\colon X \\to Y$ is the space obtained from the cylinder $X \\times [0, 1]$ by gluing its end $X \\times \\set{1}$ to $Y$ along $f$.\nIt contains $Y$ as a [[deformation retract|CEK4SC20WK]] and contains $X$ as the other end.\nSo every map is, up to [[homotopy equivalence|XZG6MTSWCN]], the inclusion of a subspace.\nThe construction is used to build mapping cones, cofibrations and long exact sequences.\n\n## Explanations\n\n### L1 human\n\nTake a tube shaped like $X$, and glue one end of the tube onto $Y$ by following $f$.\nThe other end of the tube is a copy of $X$ that sits freely in the new space.\nSliding along the tube pushes everything onto $Y$, so the new space has the same shape as $Y$.\nFor example, if $Y$ is a single point, the tube closes up into a cone on $X$.\n",
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