Unique factorization of rational homotopy types

Abstract

A nontrivial, simply connected, rational homotopy type is called irreducible, unless it is the product of two nontrivial rational homotopy types. In this paper previous results are extended by proving that every finitary, simply connected rational homotopy type having positive weights is representable as the product of a unique set of irreducible types. On the way to this unique factorization result, it is proven that (in the rational homotopy category) retracts of positive weight types again have positive weights.