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One possible answer: Stasheff proved that a (connected) space $X$ is (homotopy equivalent to) a loopspace if and only if $X$ is an algebra over the $A_\infty$ operad (or rather I should say an$A_\infty$ operad).
One possible answer: Stasheff proved that a space $X$ is a loopspace if and only if $X$ is an algebra over the $A_\infty$ operad (or rather I should say an$A_\infty$ operad).
One possible answer: Stasheff proved that a (connected) space $X$ is (homotopy equivalent to) a loopspace if and only if $X$ is an algebra over the $A_\infty$ operad (or rather I should say an$A_\infty$ operad).
One possible answer: Stasheff proved that a space $X$ is a loopspace if and only if $X$ is an algebra over the $A_\infty$ operad (or rather I should say an$A_\infty$ operad).
