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  "body": "\n## Summary\n\nThe homotopy category of a [[model category|SDTZVZ6B4Q]] is obtained by making all weak equivalences invertible.\nIt is the setting in which homotopy theory compares objects.\nTwo objects are isomorphic in it when they are connected by a chain of weak equivalences.\nFor topological spaces it can be described by CW complexes and homotopy classes of maps.\nQuillen's theorem identifies its morphisms with homotopy classes of maps between suitably replaced objects.\n\n## Explanations\n\n### L1 human\n\nIn homotopy theory, two maps are treated as equal when one can be deformed into the other.\nThe homotopy category records only this information: objects are spaces, and an arrow is a deformation class of maps.\nIn it, a disc and a point become isomorphic, since a disc can be shrunk to a point.\nThe circle and a point stay different, because the circle has a loop that cannot be shrunk.\n",
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