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  "body": "\n## Summary\n\nA map $p \\colon E \\to B$ has the homotopy lifting property with respect to a space $X$ if [[homotopies|9YA6S6HD9V]] of maps $X \\to B$ lift to $E$.\nThe lift must start at a given lift of the starting map.\nThis property defines the fibrations of homotopy theory: [[Hurewicz fibrations|Y773B7EQA7]] have it for all spaces, and [[Serre fibrations|PB9JXQ2KC3]] for all cubes.\nIt is the formal dual of the [[homotopy extension property|D42X0F1EG1]] that defines [[cofibrations|W5WS5EY8ZM]].\n\n## Explanations\n\n### L1 human\n\nPicture $E$ as a space sitting over $B$, with $p$ the shadow map.\nA homotopy in $B$ is a moving shadow, and lifting it means finding a motion in $E$ whose shadow is exactly that motion.\nThe property asks that such a motion in $E$ exists whenever the starting position is given.\nFor the covering map $\\R \\to S^1$, $t \\mapsto e^{2\\pi i t}$, a path that winds once around the circle lifts to a path in $\\R$ that moves from $0$ to $1$.\n",
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