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00925njm 22002777a 4500 dc Sopena Gilboy, Anna author 2020-07 Homotopy Theory focuses in the study of algebraic structures up to homotopy, a notion that allows to study algebraic invariants of topological and geometric origin. A classical technique in Homotopy Theory, introduced by Kadeishvili, consists in transferring multiplicative structures to certain finite dimensional-models. The price to pay is the obtention of a structure that is not associative, but only up to homotopy. On the other hand, in various topological and geometric situations, algebraic invariants are endowed with filtrations, which encode further properties of the underlying spaces. In this thesis, we study the interaction of algebraic structures up to homotopy with such filtrations by extending Kadeishvili's theory to the filtered setting. Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de categories; àlgebra homològica Algebra, Homological Categories (Mathematics) Homological algebra Dg-algebras A-infinity algebras Spectral sequences. Àlgebra homològica Categories (Matemàtica) Classificació AMS::18 Category theory; homological algebra Transferring filtered multiplicative structures in Homotopy Theory