Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8427Rational Homotopy Type of Inverse Systems in T2 CategoryMarchenkoV VКафедра математического анализа и теории функций; Российский университет дружбы народов; Peoples Friendship University of Russiawmarchenko@rambler.ruPeoples Friendship University of Russia15042011471508092016Copyright © 2011,2011A connection between Rational homotopy theory of T2 category of 1-connected spaces and homotopy theory of certain algebraic categories is established. Quillens approach is mainlybased upon functoriality. This enables one to extend the theory to the category of inverse systems. In the present paper a notion of Rational homotopy type of inverse systems of 1-connectedspaces is introduced. Its equivalence to Rational homotopy theories of certain algebraic categories is proved.rational homotopy typeinverse systemsclosed model categoryadjunction functorsequivalencesрациональный гомотопический типобратные системызамкнутая модельная категориясопряженные функторыэквивалентности