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.

The Yoneda splice product

Definition

If $ξ$ is a $p$ -fold extension of $L$ by $N$ and $η$ is a $q$ -fold extension of $M$ by $L$ , concatenate their exact sequences at $L$ . This produces a $(p + q)$ -fold extension of $M$ by $N$ . Its class is the Yoneda splice product $[ξ] ⌣ [η] \in {YExt}^{p + q} (M, N) .$ The displayed endpoint order fixes the order of the product.

Depends on

An n-fold Yoneda extension

Used by

Splicing two short exact sequences Example
Yoneda splicing is well-defined on equivalence classes Lemma
The Yoneda product is associative and unital 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)