A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted along either a left or a right adjoint. It follows that accessible model structures on locally presentable categories – ones admitting accessible functorial factorizations, a class that includes all combinatorial model structures but others besides – can be lifted along either a left or a right adjoint if and only if an essential ‘acyclicity’ condition holds. A similar result was claimed in a paper of Hess–Kędziorek–Riehl–Shipley, but the proof given there was incorrect. In this note, we explain this error and give a correction, and also provide a new statement and a different proof of the theorem which is more tractable for homotopy‐theoretic applications.

中文翻译：

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提升可访问的模型结构

相互作用的一对弱分解系统提供了Quillen模型结构。我们证明，在本地可用类别的世界中，任何具有可访问的函数分解的弱分解系统都可以沿左或右伴随提升。因此，可访问的模型结构在局部可用的类别上（允许可访问的函数分解的类别，包括所有组合模型结构的类别，除其他类别以外的类别），当且仅当基本的“非循环性”条件成立时，才可以沿左侧或右侧伴随。Hess–Kędziorek–Riehl–Shipley的论文也提出了类似的结果，但是那里给出的证据是不正确的。在本文中，我们解释了该错误并给出了更正，还提供了一条新的陈述和一个不同的定理证明，这对于同伦理论应用而言更易于处理。