False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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The bar contracting homotopy is group-equivariant

Statement

The identity-insertion contraction of the bar complex is $G$ -equivariant.

Refutation

Given: A nonidentity element $h \in G$ .

1.1given

The contraction sends $(g_{0}, \dots, g_{n})$ to $(1, g_{0}, \dots, g_{n})$ .

2.1step 1.1∎

Thus $s (h g_{0}, \dots, h g_{n}) = (1, h g_{0}, \dots)$ , whereas $h s (g_{0}, \dots, g_{n}) = (h, h g_{0}, \dots)$ ; they differ when $h \neq 1$ .

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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

Weibel, Theorem 6.5.3 (standard reference, not scraped)