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  "body": "\n## Summary\n\nA morphism $i$ has the left lifting property with respect to a morphism $p$ when every suitable commutative square has a diagonal filler.\nThe square has $i$ on its left side and $p$ on its right side.\nEquivalently, $p$ has the right lifting property with respect to $i$.\nLifting properties define fibrations and cofibrations in homotopy theory and in model categories, and they describe many classes of maps by a single test.\nWhen the filler is always unique, $i$ and $p$ are called orthogonal.\n\n## Explanations\n\n### L1 human\n\nPicture a square of four maps: $u$ along the top, $v$ along the bottom, $i$ on the left and $p$ on the right, with the square commuting.\nA lift is a diagonal map from the bottom left corner to the top right corner that keeps both triangles commuting.\nIn topology, the [[homotopy lifting property|G4QDM01P6J]] is of this kind: a homotopy in the base lifts to the total space once its start is lifted.\nIn sets, a surjection has the right lifting property with respect to the inclusion of the empty set into a point: every point of the target has a preimage.\n",
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