Suppose X is a loop space; by this we mean there is some space $Y$ with $\Omega Y \simeq X$.
Under what assumptions is (the homotopy type of) $Y$ unique?
Suppose X is a loop space; by this we mean there is some space $Y$ with $\Omega Y \simeq X$.
Under what assumptions is (the homotopy type of) $Y$ unique?