Differential graded versus Simplicial categories
K-Theory and Homology
2007-11-27 v1 Algebraic Topology
Abstract
We construct a zig-zag of Quillen adjunctions between the homotopy theories of differential graded and simplicial categories. In an intermediate step we generalize Shipley-Schwede's work on connective DG algebras by extending the Dold-Kan correspondence to a Quillen equivalence between categories enriched over positive graded chain complexes and simplicial k-modules. As an application we obtain a conceptual explanation of Simpson's homotopy fiber construction.
Cite
@article{arxiv.0711.3845,
title = {Differential graded versus Simplicial categories},
author = {Goncalo Tabuada},
journal= {arXiv preprint arXiv:0711.3845},
year = {2007}
}
Comments
22 pages