Rational homotopy theory of spaces 1-connected by shape (Q2011286)

In this paper the author defines a (strong) rational shape category of spaces 1-connected by shape; he also provides a generalization of similar results introduced by D. Quillen. A rational shape type and a string rational shape type are defined for the class of spaces 1-connected by shape (a natural generalization of the class of 1-connected spaces for which the rational homotopy theory was constructed by D. Quillen). Using the category of inverse systems, the results of D. Quillen on the equivalence of homotopy theories are extended for the class of spaces 1-connected by shape. The paper is organised in nine sections: Introduction, Rational theory of CW complexes, Inverse systems and the category of shapes, Closed model categories and homotopy theory by D. Quillen, Quillen functors, Bousfield-Kan functor \(Q_{\infty}\), Rational shape category, Isomorphism of the pro-categories as closed model categories, Strong rational shape category.