Idempotent functors that preserve cofiber sequences and split suspensions (Q351695)

Following results of Quillen and Sullivan in which noncomputational theorems about rationalization are proved (they applied the algebraic machinery to the basic homotopy theoretical properties), in this paper the author proposes a homotopy theoretical characterization of the rationalization functor. He shows that \(L_f\) is the only \(f\)-localization functor of simply connected spaces that preserves cofiber sequences and splits suspensions.NEWLINENEWLINEThe main result of the paper is the Theorem 2: The restriction of a localization functor \(L_f\) to simply connected spaces is rationalization if and only if the following three conditions hold: \(L_f (S^2)\) is nontrivial and simply connected, \(L_f\) preserves cofiber sequences of simply connected finite complexes and for each simply connected finite complex \(K\), there is a \(k\) such that the \(k\)-sum of \(L_f (K)\) splits as a wedge of copies of \(L_f (S^n)\) for various of \(n\).