# Bar constructions and Quillen homology of modules over operads

@article{Harper2008BarCA,
title={Bar constructions and Quillen homology of modules over operads},
author={John E. Harper},
journal={Algebraic \& Geometric Topology},
year={2008},
volume={10},
pages={87-136}
}
• John E. Harper
• Published 16 February 2008
• Mathematics
• Algebraic & Geometric Topology
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…
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