DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

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.

Supplied injective resolution data

Definition

Let $A$ be an abelian category, and let $D$ be a class of objects of $A$ .

A supplied injective resolution datum on $D$ assigns to each $A \in D$ a specific injective resolution $A \to I^{∙} (A)$ in the sense of Injective resolutions in an abelian category.

Again this is part of the input data. It keeps the chosen coaugmented resolutions visible rather than hiding a global selection claim in the background.

Depends on

Dependency tree · 2 levels

Sources

Charles A. Weibel, An Introduction to Homological Algebra, Chapter 2 `Derived Functors`