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  "body": "\n## Summary\n\nA weak homotopy equivalence is a continuous map that induces a bijection on path components and isomorphisms on all [[homotopy groups|P976WYEFMB]], at every base point.\nEvery [[homotopy equivalence|XZG6MTSWCN]] is a weak homotopy equivalence, and between CW complexes the converse holds by the [[Whitehead theorem|6P1E2FJPSD]].\nEvery space is weakly equivalent to a CW complex, so weak equivalences are the natural notion of sameness in homotopy theory.\nThey are the model for weak equivalences in abstract homotopy theory, such as in model categories.\n\n## Explanations\n\n### L1 human\n\nHomotopy groups only see a space through the spheres that map into it.\nA weak homotopy equivalence is a map that looks like an equivalence to every sphere.\nFor nice spaces this is the same as a true equivalence up to deformation.\nFor strange spaces, such as the Warsaw circle, a map to a point can fool every sphere and still not be an equivalence.\n",
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