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Published online by Cambridge University Press: 19 December 2024
In this chapter we define and deduce the first principles of the homotopy category of an abelian model structure. The most fundamental result is that it is the localization category obtained by forcing the weak equivalences to become isomorphisms. Moreover, morphisms in the homotopy category may be realized as homotopy equivalence classes of morphisms from a cofibrant replacement of the source object to a fibrant replacement of the target object. It is also shown how coproducts and products may be constructed in the homotopy category.
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