Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Ok, thanks, but I assume that for the homotopy category you have to elaborate more the argument, because having nonzero cohomology only at degree zero doesn't mean that the complex is concentrated on degree zero...
I follow Greg's argument, but I don't understand why you reach a contradiction, since $\mathbb{Z}/p^2\mathbb{Z}$ is idecomposable in the category of abelian groups, but in the homotopy category it may not be...
