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- W3149226875 abstract "In this chapter, we introduce the notion of pointed model categories and show that the homotopy category of a pointed model category has a suspension functor with an adjoint called the loop functor. This suspension functor is a generalisation of the standard notion of (reduced) suspension of pointed topological spaces. We shall also see that, in the case of chain complexes over a ring, this suspension functor is modelled by the shift functor. With these constructions in place, we can define the notion of a stable model category. The suspension and loop functors allow us to define cofibre and fibre sequences in an arbitrary pointed model category. These sequences are a generalisation of cofibre and fibre sequences for pointed spaces category of a pointed model category and are a useful aid to calculations. When the model category is also stable, these cofibre and fibre sequences form the basis of important additional structure on the homotopy category." @default.
- W3149226875 created "2021-04-13" @default.
- W3149226875 creator A5032015603 @default.
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- W3149226875 date "2020-03-26" @default.
- W3149226875 modified "2023-09-23" @default.
- W3149226875 title "Sequential Spectra and the Stable Homotopy Category" @default.
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- W3149226875 doi "https://doi.org/10.1017/9781108636575.003" @default.
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