We provide an enhancement of Shipley's algebraicization theorem which behaves better in the context of commutative algebras. This involves defining flat model structures as in Shipley and Pavlov-Scholbach, and showing that the functors still provide Quillen equivalences in this refined context. The use of flat model structures allows one to identify the algebraic counterparts of change of groups functors, as demonstrated in forthcoming work of the author.

中文翻译：

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平坦度和希普利代数化定理

我们提供了 Shipley 代数化定理的增强，它在交换代数的上下文中表现得更好。这包括像 Shipley 和 Pavlov-Scholbach 一样定义平面模型结构，并表明函子在这种精炼的上下文中仍然提供 Quillen 等价。平面模型结构的使用允许人们识别群函子变化的代数对应物，正如作者即将开展的工作所证明的那样。