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Operads, algebras and modules in model categories and motives. (English) Zbl 1103.18300

Bonn: Univ. Bonn. Mathematisch-Naturwissenschaftliche Fakultät (Dissertation). 77 p. (2001).
Summary: In the first part of this thesis the homotopy theory of operads, algebras over operads and modules over operad algebras is developed in the context of cofibrantly generated symmetric monoidal model categories. It is shown that under mild hypotheses such categories form so-called semi model categories, a slightly weakened notion of model category. We particularly analize \(E\)-infinity operads, \(E\)-infinity algebras and modules over \(E\)-infinity algebras, generalizing the theory of \(S\)-algebras and \(S\)-modules.
In the second part we apply this theory to model categories of motivic origin and describe a special construdion what we call limit motives (analoguous to limit Hodge structures).

MSC:

18D50 Operads (MSC2010)
14F42 Motivic cohomology; motivic homotopy theory
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
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