Differential graded versus simplicial categories

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We establish a connection between differential graded and simplicial categories byconstructing 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 aQuillen equivalence between categories enriched over non-negatively graded complexesand categories enriched over simplicial modules. As an application, we obtain a simplecalculation 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.
Original languageUnknown
Pages (from-to)563-593
JournalTopology and its Applications
Volume157
Issue number3
DOIs
Publication statusPublished - 1 Jan 2010

Cite this

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Differential graded versus simplicial categories. / Tabuada, Gonçalo Jorge Trigo Neri.

In: Topology and its Applications, Vol. 157, No. 3, 01.01.2010, p. 563-593.

Research output: Contribution to journalArticle

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AB - We establish a connection between differential graded and simplicial categories byconstructing 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 aQuillen equivalence between categories enriched over non-negatively graded complexesand categories enriched over simplicial modules. As an application, we obtain a simplecalculation 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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