Exact dg categories I: Foundations
Abstract
We introduce the notion of exact dg category, which provides a differential graded enhancement of Nakaoka–Palu's notion of extriangulated category. We give a definition in complete analogy with Quillen's but where the category of kernel-cokernel pairs is replaced with a more sophisticated homotopy category. We introduce the notion of stable dg category, and prove that the 𝐻 0 -category of an exact dg category 𝒜 is triangulated if and only if 𝒜 is stable. We illustrate our theory with several examples including the homotopy category of two-term complexes and Amiot's fundamental domain for generalized cluster categories.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 489
- Pages
- 110809–110809
- Publication date
- 28 January 2026
- Language
- EN