Operads, Algebras and Modules in Model Categories and Motives

Abstract

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.<br /> In the second part we apply this theory to model categories of motivic origin and describe a special construction what we call limit motives (analoguous to limit Hodge structures).