0PBZ Proposition 7.4.33. The functor FF induces an isomorphism of differential pointed categories ℋn→∼𝒮M∙(S1){\mathcal{H}}_{n}\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{S}}^{\bullet}_{M}(S^{1}). It restricts to isomorphisms of differential pointed categories ℋn+→∼𝒮M∙(S˙1),ℋn++→∼𝒮M∙(S→1),ℋnf→∼𝒮M∙(I) and ℋnf++→∼𝒮M∙(I→).{\mathcal{H}}_{n}^{+}\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{S}}^{\bullet}_{M}(\dot{S}^{1}),\ {\mathcal{H}}_{n}^{++}\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{S}}^{\bullet}_{M}(\vec{S}^{1}),\ {\mathcal{H}}_{n}^{f}\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{S}}^{\bullet}_{M}(I)\text{ and }{\mathcal{H}}_{n}^{f++}\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}{\mathcal{S}}^{\bullet}_{M}(\vec{I}).