Differential graded versus Simplicial categories
Abstract
Description
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.
22 pages
22 pages