mapCocycles₂ — Mathlib

English

Second cocycles map is defined similarly to the first, now on Z².

Русский

Отображение кокайклов во втором когоменте аналогично первому, на уровне Z².

LaTeX

$$$ mapCocycles_2: \mathrm{ModuleCat}.of(k, \mathrm{cocycles}_2(A)) \to \mathrm{ModuleCat}.of(k, \mathrm{cocycles}_2(B)) $$$

Lean4

/-- Given a group homomorphism `f : G →* H` and a representation morphism `φ : Res(f)(A) ⟶ B`,
this is induced map `Z²(H, A) ⟶ Z²(G, B)`. -/
noncomputable abbrev mapCocycles₂ : ModuleCat.of k (cocycles₂ A) ⟶ ModuleCat.of k (cocycles₂ B) :=
  ShortComplex.cyclesMap' (mapShortComplexH2 f φ) (shortComplexH2 A).moduleCatLeftHomologyData
    (shortComplexH2 B).moduleCatLeftHomologyData

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