Completing the Cohomological Extension Package: Section Cocycles and Splitting Criterion for Mathlib

April 5, 2026Open Access

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This work aims to formalize the relationships between group extensions and cohomology classes, specifically H^1 and H^2.
Documenting explicit TODOs in Mathlib
Proposing section cocycles for group extensions
Detailing the splitting criterion for trivial cocycles
Verifying all theorems with Lean type checker
Introduced the section cocycle associated with group extensions
Defined the splitting criterion as splits_iff_trivial_cocycle
Created supporting functions like section difference and conjugation actions
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Technical note documents the development of section cocycles and splitting criteria for group extensions, suggesting foundational improvements.

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Nova Spivack (2026) studied this question.

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