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False statementConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06
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Group cohomology is the derived functor of coinvariants

Statement

Group cohomology is the derived functor of coinvariants.

Refutation

Given: The definitions of group cohomology and group homology.

1.1

Coinvariants are right exact, so their left derived functors are indexed homologically.

given
2.1

Those derived functors are Hn(G;M); cohomology is instead the right derived functor of the left exact invariants functor.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

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Sources