Bar constructions and Quillen homology of modules over operads

被引:10
作者
Harper, John E. [1 ,2 ]
机构
[1] Ecole Polytech Fed Lausanne, Inst Geometrie Algebre & Topol, CH-1015 Lausanne, Switzerland
[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
来源
ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2010年 / 10卷 / 01期
关键词
MODEL CATEGORIES; HOMOTOPY-THEORY; ALGEBRAS; COHOMOLOGY;
D O I
10.2140/agt.2010.10.87
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical proof after showing that certain homotopy colimits in algebras and modules over operads can be easily understood. A key result here, which lies at the heart of this paper, is showing that the forgetful functor commutes with certain homotopy colimits. We also prove analogous results for algebras and modules over operads in unbounded chain complexes.
引用
收藏
页码:87 / 136
页数:50
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