DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Injective dimension of an object

Definition

Assume injective resolutions are supplied or exist in the relevant class. The injective dimension of $N$ is $id (N) = \inf {d \geq 0 : N has an injective resolution of length d},$ with value $\infty$ if there is no finite such resolution. A length-zero injective resolution exists exactly when $N$ is injective.

Depends on

Dependency tree · 2 levels

Sources

Charles A. Weibel, An Introduction to Homological Algebra, Chapters 3–4