### Definition ### A H-Space consists of * A type $A$, * A basepoint $e:A$ * A binary operation $\mu : A \to A \to A$ * for every $a:A$, equalities $\mu(e,a)=a$ and $\mu(a,e)=a$ ### Lemma ### Let $A$ be a connected H-space. Then for every $a:A$, the maps $\mu(a,-),\mu(-,a):A \to A$ are equivalences.