English

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.

Keywords

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

R2 v1 2026-06-21T09:46:54.719Z