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Spectra in model categories and applications to the algebraic cotangent complex. (English) Zbl 0888.55010
The paper is mainly concerned with stable homotopy theory in an abstract setting. The notion of spectrum is introduced in a pointed closed simplicial model category in the sense of D. Quillen [Homotopical algebra, Lect. Notes Math. 43 (1967; Zbl 0168.20903)]. It is shown how the category of spectra forms a model category. For a linear model category, it is made precise that the passage to spectra gives the same homotopy theory. (A model category is called linear, if for any object \(X\) the adjunction map from \(X\) to the loops on the suspension of \(X\) is an isomorphism in the homotopy category.) Applications to the model category of simplicial modules over a fixed simplicial ring are included.
Reviewer: K.H.Kamps (Hagen)

MSC:
55U35 Abstract and axiomatic homotopy theory in algebraic topology
18G55 Nonabelian homotopical algebra (MSC2010)
18G30 Simplicial sets; simplicial objects in a category (MSC2010)
55P42 Stable homotopy theory, spectra
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