Rational Homotopy Type of Inverse Systems in T2 Category

Abstract

A 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.