Rational homotopy theory of spaces 1-connected by shape

A rational shape type and a strong rational shape type are defined for the class of spaces 1-connected by shape. This class is a natural generalization of the class of 1-connected spaces for which the rational homotopy theory was constructed in work [10]. With the use of the category of inverse systems, the result in [10] on the equivalence of homotopy theories is extended onto the class of spaces 1-connected by shape. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.