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Every homotopy theory of simplicial algebras admits a proper model

Charles Rezk
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Abstract

We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By ``simplicial algebra'' we mean any category of algebras over a simplicial algebraic theory, which is allowed to be multi-sorted. The results have applications to the construction of localization model category structures.

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Charles Rezk. 2000-03-10. Every homotopy theory of simplicial algebras admits a proper model. https://arxiv.org/abs/math/0003065

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