Differential Graded Categories are k-linear Stable Infinity Categories

Abstract

We describe a comparison between pretriangulated differential graded categories and certain stable infinity categories. Specifically, we use a model category structure on differential graded categories over k (a field of characteristic 0) where the weak equivalences are the Morita equivalences, and where the fibrant objects are in particular pretriangulated differential graded categories. We show the underlying infinity category of this model category is equivalent to the infinity category of k-linear stable infinity categories.

Characteristic 0 assumption has been removed. Main arguments are significantly revised. Several errors corrected. arXiv admin note: substantial text overlap with arXiv:1001.2282 by other authors

References in corpus (1)

• Higher Topos Theory

Cited by in corpus (21)

• The nonequivariant coherent-constructible correspondence for toric stacks
• Non-Archimedean analytic geometry as relative algebraic geometry
• Enhancing the filtered derived category
• Topological Fukaya category and mirror symmetry for punctured surfaces
• Calabi-Yau structures on topological Fukaya categories
• The symplectic geometry of higher Auslander algebras: Symmetric products of disks
• Simplicial nerve of an A-infinity category
• Generators in formal deformations of categories
• Motivic Realizations of Singularity Categories and Vanishing Cycles
• The Fukaya category pairs with Lagrangian cobordisms exactly
• The derived contraction algebra
• Ginzburg algebras of triangulated surfaces and perverse schobers
• Nilpotent invariance of semi-topological K-theory of dg-algebras and the lattice conjecture
• On nilpotent extensions of $\infty$-categories and the cyclotomic trace
• Intrinsic mirror symmetry and categorical crepant resolutions
• Equivariant localization and completion in cyclic homology and derived loop spaces
• On the tensor product of well generated dg categories
• Differential calculus of Hochschild pairs for infinity-categories
• Some properties of the A${}_{\infty }$-nerve
• Cycle maps on cohomology theories for dg-categories and their applications
• Versal dg deformation of Calabi--Yau manifolds