Reduced homology sends wedge sums of good pointed spaces to direct sums.Suggest a slogan
Let \((X_\alpha, x_\alpha)\) be pointed spaces such that each \((X_\alpha, \theset{x_\alpha})\) is a good pair. Then the inclusions \(X_\alpha\injects\bigvee_\alpha X_\alpha\) induce an isomorphism \[ \bigoplus_\alpha \tilde H_n(X_\alpha) \xrightarrow{\ \sim\ } \tilde H_n\qty{\bigvee_\alpha X_\alpha} \] for every \(n\) [@Hat02].
The wedge sum \(\bigvee_\alpha X_\alpha\) is the coproduct in the category of pointed topological spaces.