Differential graded versus Simplicial categories

Details Differential graded versus Simplicial categories Differential graded versus Simplicial categories

2007-11-24

arxiv.org/abs/0711.3845v1

Mathematics

K-Theory and Homology

22 pages

Scientific paper

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.

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