definition A.397 Cochains and the differential

open in the book · appendices/A-long-proofs.tex:19413 · p. 2985

ground object -- no derivation owed

Rests on

depends_on definition 14.75 The classifying group ¶
- depends_on definition 14.74 Coboundary and triviality ¶
  - depends_on proposition 14.73 The extension datum is a $2$-cocycle ¶
    - depends_on definition 14.72 Central extension ¶
    - proves proof ch:12-lie-groups-fibre-bundles@proof-35 ¶
- depends_on proposition 14.73 The extension datum is a $2$-cocycle ¶ ↺

Supports

depends_on lemma A.398 The differential squares to zero in the degrees used ¶
depends_on theorem A.403 Vanishing when the Casimir is invertible ¶
- depends_on theorem A.410 Whitehead's first and second lemmas ¶
  - depends_on corollary A.411 Semisimple algebras admit no nontrivial extension ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	The classifying group	declared	appendices/A-long-proofs.tex:19445
`depends_on`	←	The differential squares to zero in the degrees used	declared	appendices/A-long-proofs.tex:19454
`depends_on`	←	Vanishing when the Casimir is invertible	declared	appendices/A-long-proofs.tex:19638