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  "body": "\n## Summary\n\nA cofibration is a continuous map $i \\colon A \\to X$ along which homotopies extend: it has the [[homotopy extension property|D42X0F1EG1]] for every target space.\nInclusions of subcomplexes of CW complexes are the main examples.\nCofibrations are well behaved for gluing, and for a cofibration the quotient $X / A$ has the homotopy type of the mapping cone.\nThey are dual, in the sense of [[Eckmann–Hilton duality|1EK3355WMC]], to fibrations.\n\n## Explanations\n\n### L1 human\n\nA cofibration is a nicely attached subspace.\nWhenever a map on the whole space is given and you deform it on the subspace, the deformation can be carried along on the whole space.\nThe boundary circle of a disk is attached in this nice way.\nAn open interval inside a closed interval is not, because its closure adds new points.\n",
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