mapShortComplexH2_comp — Mathlib

English

Exactness is established by showing Im(f) = Ker(g).

Русский

Точность достигается доказательством равенства образа f и ядра g.

LaTeX

$$$\text{H1InfRes_exact}$$$

Lean4

@[reassoc]
theorem mapShortComplexH2_comp {G H K : Type u} [Group G] [Group H] [Group K] {A : Rep k K} {B : Rep k H} {C : Rep k G}
    (f : H →* K) (g : G →* H) (φ : (Action.res _ f).obj A ⟶ B) (ψ : (Action.res _ g).obj B ⟶ C) :
    mapShortComplexH2 (f.comp g) ((Action.res _ g).map φ ≫ ψ) = mapShortComplexH2 f φ ≫ mapShortComplexH2 g ψ :=
  rfl

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