Any map that factors through a contractible space is nullhomotopic.Suggest a slogan
Let \(X\), \(Y\) and \(Z\) be topological spaces with \(Z\) contractible, and let \(\tilde f\colon X\to Z\) and \(p\colon Z\to Y\) be continuous maps. Then \(f \coloneqq p\circ \tilde f\colon X\to Y\) is nullhomotopic.