The Rational Homotopy Category of Simply Connected Spaces

Abstract

Rational homotopy theory is homotopy theory up to rational homotopy equivalence. In this chapter we show that rational homotopy of 1-connected spaces fits into the general framework introduced in the previous chapter. We show how the categories CDA_* and DL introduced in chapter 4 model the category of 1-connected rational CW-spaces; more precisely, the homotopy categories of CDA_* and DL respectively, are equivalent to the homotopy category of 1-connected rational CW-spaces.