Differential Graded Categories are k-linear Stable Infinity Categories

2013/08/12 by Lee Cohn, Cohn, Lee · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1308.2587

openalex publication_date 2013/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On a tamely ramified local relative Langlands conjecture via categorical representations
• The Fukaya category pairs with Lagrangian cobordisms exactly
• The derived contraction algebra

Related

• Remarks on the equivalence between differential graded categories and A-infinity categories
• On differential graded categories
• k-linear Morita theory
• Stable Infinity Categories
• Derived categories of NDG categories