Every homotopy theory of simplicial algebras admits a proper model

Charles Rezk

doi:10.1016/S0166-8641(01)00057-8

Every homotopy theory of simplicial algebras admits a proper model

Charles Rezk

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	65-94
Number of pages	30
Journal	Topology and its Applications
Volume	119
Issue number	1
DOIs	https://doi.org/10.1016/S0166-8641(01)00057-8
State	Published - Mar 31 2002

Keywords

Algebraic theories
Model categories
Simplicial algebras

ASJC Scopus subject areas

Geometry and Topology

Online availability

10.1016/S0166-8641(01)00057-8

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title = "Every homotopy theory of simplicial algebras admits a proper model",

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.",

keywords = "Algebraic theories, Model categories, Simplicial algebras",

author = "Charles Rezk",

note = "Funding Information: E-mail address: rezk@math.uiuc.edu (C. Rezk). 1Current address: Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, IL 61801, USA. The author was supported by an AMS Centennial Fellowship, and by NSF grant DMS 97-29992.",

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PY - 2002/3/31

Y1 - 2002/3/31

N2 - 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.

AB - 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.

KW - Algebraic theories

KW - Model categories

KW - Simplicial algebras

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JO - Topology and its Applications

JF - Topology and its Applications

IS - 1

ER -

Every homotopy theory of simplicial algebras admits a proper model

Abstract

Keywords

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