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  "body": "\n## Summary\n\nLet $\\mathcal{A}$ be an additive category.\nThe homotopy category of chain complexes $K(\\mathcal{A})$ has the [[chain complexes|WQ82C0M3QB]] as objects and the [[chain maps|HTK9WQZJ1G]] modulo [[chain homotopy|4EBHAWJJ8C]] as morphisms.\nIn it, chain homotopy equivalences become isomorphisms.\nIt is a [[triangulated category|T2V7GJJ2EN]], and the [[derived category|5ST7NVJFSM]] of an abelian category is obtained from it by inverting the quasi-isomorphisms.\n\n## Explanations\n\n### L1 human\n\nTwo chain maps that are chain homotopic induce the same map on homology, so for many purposes they are the same.\nThe homotopy category identifies them.\nA complex that can be contracted to zero, such as $0 \\to \\Z \\xrightarrow{\\id} \\Z \\to 0$, becomes isomorphic to the zero complex.\nIt is the algebraic analogue of the homotopy category of spaces, where homotopic maps are identified.\n",
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