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Since the birth of rational homotopy theory, the possibility of extending the Quillen approach –  in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version.

In this book, the authors develop new tools to address these problems. Working with...