coboundaries₂ — Mathlib

English

First coboundaries lie inside the first cocyles: B¹(G,A) ⊆ Z¹(G,A).

Русский

Границы B¹(G,A) подмножество Z¹(G,A).

LaTeX

$$$$ coboundaries_1(A) \\le cocycles_1(A). $$$$

Lean4

/-- The 2-coboundaries `B²(G, A)` of `A : Rep k G`, defined as the image of the map
`Fun(G, A) → Fun(G × G, A)` sending `(f, (g₁, g₂)) ↦ ρ_A(g₁)(f(g₂)) - f(g₁g₂) + f(g₁).` -/
def coboundaries₂ : Submodule k (G × G → A) :=
  LinearMap.range (d₁₂ A).hom

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