Differential graded versus simplicial categories |
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Authors: | Gonçalo Tabuada |
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Institution: | Departamento de Matemática and CMA, FCT-UNL, Quinta da Torre, 2829-516 Caparica, Portugal |
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Abstract: | We establish a connection between differential graded and simplicial categories by constructing a three-step zig-zag of Quillen adjunctions relating the homotopy theories of the two. In an intermediate step, we extend the Dold-Kan correspondence to a Quillen equivalence between categories enriched over non-negatively graded complexes and categories enriched over simplicial modules. As an application, we obtain a simple calculation of Simpson's homotopy fiber, which is known to be a key step in the construction of a moduli stack of perfect complexes on a smooth projective variety. |
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Keywords: | Dg category Simplicial category Dold-Kan correspondence Quillen model structure |
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