differential graded category

dg-范畴

Algebra & Algebraic Geometry · Research · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: dg category · DG category

Translation evidence: Literature usage

Meaning in context

A category enriched in cochain complexes over a commutative ring, with associative unital degree-zero composition that is a map of complexes.

在交换基环上的上链复形中充实、复合满足结合律和单位律且与微分相容的范畴。

Example

A dg algebra is a dg category with one object.

Usage and distinctions

H0H^0 discards chain-level data; a triangulated category alone is not a supplied dg enhancement.

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Definition sources

  1. Bernhard Keller — On Differential Graded Categories§2.2, Differential graded categories · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法 卷二§7.4 案例研究: dg-范畴的闭结构 · Checked 2026-10-14
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