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  "body": "\n## Summary\n\nLet $(X, x_0)$ be a [[pointed space|T9DG8DDE75]] and $PX$ the space of paths that start at $x_0$.\nThe path space fibration is the map $PX \\to X$ that sends each path to its end point.\nIt is a fibration, its total space $PX$ is contractible, and its fiber over $x_0$ is the [[loop space|2JFF5F3EGF]] $\\Omega X$.\nFrom its [[long exact sequence of homotopy groups|E0RV5D1GQ0]] one gets $\\pi_n(\\Omega X) \\cong \\pi_{n+1}(X)$.\nIt plays the role of a universal bundle for loops and is the basic input of the Serre spectral sequence computations of loop spaces.\n\n## Explanations\n\n### L1 human\n\nFix a home point $x_0$ in $X$.\nA point of the path space is a walk in $X$ that starts at home, and the map records where the walk ends.\nAll walks can be shrunk back to the walk that stays at home, so the path space has no shape of its own.\nThe walks that end at home are the loops, so the loops form the fiber over $x_0$.\n",
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