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.

Right derived objects relative to supplied injective resolution data

Definition

Let $I$ be a supplied injective resolution datum on a class $D$ of objects in an abelian category $A$ , and let $F : A \to B$ be an additive functor to an abelian category $B$ .

For $A \in D$ and $n \in Z$ , the $n$ th right derived object of $F$ relative to $I$ at $A$ is $R_{I}^{n} F (A) : = H^{n} ⁣ (F (I (A)_{d e l})),$ where $I (A)_{d e l}$ is the deleted injective resolution from Deleted resolutions.

The superscript records the supplied injective datum. This page keeps that data visible instead of suppressing it into an unstated global choice.

Depends on

Dependency tree · 2 levels

Sources

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