On the homotopy sets of simply connected rational CW-complexes

Let X and Y be two simply connected rational CW-complexes, and \(n \in \mathbb{N}\). We study the homotopy set \([P^nX, P^nY]\), where PⁿX and PⁿY are the \(n\)-th Postnikov sections of X and Y, respectively. An equivalence relation is defined on this set, revealing connections with the cohomology groups. This approach uses rational homotopy theory to uncover new structural insights.