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.

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AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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An n-fold Yoneda extension

Definition

For $n \geq 1$ , an $n$ -fold extension of $M$ by $N$ is an exact sequence $0 ⟶ N ⟶ E_{n - 1} ⟶ \dots ⟶ E_{0} ⟶ M ⟶ 0.$ For $n = 1$ this is the preceding notion of a short extension. The left endpoint is always the second Ext variable.

Depends on

An extension of an object by an object in an abelian category

Used by

Equivalence of n-fold extensions Definition
The Yoneda splice product Definition
Higher Yoneda Ext agrees with derived Ext Theorem

Dependency tree · two levels

2 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Charles A. Weibel, An Introduction to Homological Algebra, Chapters 3–4 (standard reference, not scraped)