A model categorical approach to group completion of E_n-algebras
Manfred Stelzer
TL;DR
This paper introduces a model categorical framework for the group completion of E_n-algebras, establishing a functor that enhances the algebraic structure within a homotopical setting.
Contribution
It constructs a group completion functor Q for E_n-algebras and proves it induces a Bousfield-Friedlander model category structure.
Findings
Q defines a functorial group completion in E_n-algebras
Q induces a Bousfield-Friedlander model structure
The approach applies to simplicial set-based E_n-algebras
Abstract
A group completion functor Q is constructed in the category of algebras in simplicial sets over a cofibrant E_n-operad M. It is shown that Q defines a Bousfield-Friedander simplicial model category on M-algebras.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models