 An embedding is a homomorphism where the involved functions are injective and the second condition works in both directions. An isomorphism is an embedding where the defining maps are bijections. When the function \(\pi\) is an isomorphism one says that \(\mathcal{A}\) and \(\mathcal{A}^{\prime }\) are isomorphic and writes \(\mathcal{A}\cong \mathcal{A}^{\prime }\).