I am studying homotopy theory and I would like to understand better what it means for a category to be stable.
For instance, the book I'm studying says that
"the categories CW∗ and CCh+ have very similar homotopical properties. On the other hand, there is a primary difference between them: while in both we have canonical reduced suspension functor Σ and loop space functor Ω, the cochain complex are “stable” under these functors while CW-complexes are not",
where CW∗ is the category of CW-complexes and CCh+ is the category of cochain complexes over some communtative ring.
I don't know a lot about classical algebraic topology (I went directly to the higher categorical approach). Thus, it would be quite helpful if someone explained the above statement to me.