LemmaStatement: Literature-sourcedProof: AI-generatedPipeline-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.

Corestriction is independent of coset representatives

Statement

The corestriction map for a finite-index subgroup $H \leq G$ does not depend on the chosen coset transversal.

Proof

Given: Two transversals $T, T^{'}$ for the left cosets $G / H$ .

1.1given

For every $t \in T$ there are unique $t^{'} \in T^{'}$ and $h_{t} \in H$ with $t = t^{'} h_{t}$ . If $m \in M^{H}$ , then $t m = t^{'} h_{t} m = t^{'} m$ . Thus the two representative sums define the same degree-zero norm $N_{H}^{G} : M^{H} \to M^{G}$ .

2.1step 1.1∎

Corestriction is defined as the unique morphism of universal cohomological delta functors extending that norm. Since the two transversals give the same degree-zero map, uniqueness forces their corestriction maps to agree in every degree.

Depends on

Used by

Corestriction after restriction multiplies by the index Theorem

Dependency tree · two levels

11 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

Löh, Remark 1.7.14 (standard reference, not scraped)