Every homotopy theory of simplicial algebras admits a proper model

By Charles Rezk. 2000

59 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/de06c36d174610b3334c66c7d3d4f8444165d904

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Derived smooth manifolds (2008, methodology): “(Note that, by [24], we could have used a simplicial version of the theory to obtain a proper model of strict algebras, but this model is more difficult to use for our purposes.”
Long knots and maps between operads (2010, methodology): “For our approach to the homotopy theory of operads we are deeply indebted to the results on Rezk [22]”
RESOLUTION OF COLOURED OPERADS AND RECTIFICATION OF HOMOTOPY ALGEBRAS (2005, methodology): “Fresse [14]). A coherent theory of such resolutions is provided by a Quillen homotopy theory of operads, as established by Hinich [16] for operads in chain complexes, by Rezk [ 26 ] for simplicial operads, and by Spitzweck [29] and the authors [3] for operads in general monoidal model categories.”