The goal of this paper is to establish an equivalence of profinite completions of pro-spaces in model category theory and in \(\infty \)-category theory. As an application, we show that the author’s comparison theorem for algebro-geometric objects in the setting of model categories recovers that of David Carchedi in the setting of \(\infty \)-categories.

中文翻译：

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等价的有限完成

本文的目标是在模型范畴论和\(\infty \)范畴论中建立亲空间的有限完成等价。作为一个应用，我们展示了作者在模型类别设置中的代数几何对象比较定理恢复了 David Carchedi 在\(\infty \)类别设置中的比较定理。