On maps into a co-\(H\)-space (Q1268694)

Let \(f:X\to Y\) be a based map of a CW-complex \(X\) into a co-\(H\)-space \(Y\). The authors prove that \(X\) admits a co-\(H\)-structure such that \(f\) is a co-\(H\)-map provided \(\dim X\leq\text{conn} f+ \min\{\text{conn} X, \text{conn} Y\}\). Given a map \(f:X\to Y\) between 1-connected co-\(H\)-spaces, a similar condition ensures that it is a co-\(H\)-map. Finally the authors show that a co-\(H\)-structure on \(X\) determines and is determined by co-\(H\)-structures on the skeleta \(X^{(n)}\) or on the stages \(X_n\) of the homology decomposition of \(X\).