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  "body": "\n## Summary\n\nA path homotopy is a deformation of one path into another with both end points held fixed.\nIt is a [[homotopy relative|ADDS6HE5SV]] to the end points $\\set{0, 1}$ of the interval $[0, 1]$.\nClasses of paths up to path homotopy form the [[fundamental group|S1XK3HXHFX]] and the [[fundamental groupoid|ZBHGXJF24E]].\n\n## Explanations\n\n### L1 human\n\nThink of a path as a string from a point $p$ to a point $q$, with both ends nailed down.\nA path homotopy moves the string around without moving the nails and without cutting it.\nIn the plane, any two paths from $p$ to $q$ are path homotopic.\nIn the plane without the origin, a path that passes above the origin and one that passes below it are not.\n",
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