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  "body": "\n## Summary\n\nTwo continuous maps $f, g \\colon X \\to Y$ are homotopic, written $f \\simeq g$, when there is a [[homotopy|9YA6S6HD9V]] from $f$ to $g$.\nBeing homotopic is an equivalence relation on the set of continuous maps from $X$ to $Y$.\nIts equivalence classes are the homotopy classes, and the set of them is written $[X, Y]$.\nAlgebraic topology studies spaces through such sets of homotopy classes.\n\n## Explanations\n\n### L1 human\n\nTwo maps are homotopic when one can be slid continuously into the other inside $Y$.\nHomotopy forgets the fine details of a map and keeps only its shape up to deformation.\nFor example, every two maps into $\\R^n$ are homotopic, by moving each point along a straight segment.\nTwo loops in the circle that wind around a different number of times are not homotopic.\n",
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