cocyclesIso₀_hom_comp_f — Mathlib

English

A precise equality of morphisms: (cocyclesIso0 A).hom ∘ (shortComplexH0 A).f = iCocycles A 0 ∘ (cochainsIso0 A).hom.

Русский

Точная равенство отображений: (cocyclesIso0 A).hom ∘ (shortComplexH0 A).f = iCocycles A 0 ∘ (cochainsIso0 A).hom.

LaTeX

$$$(cocyclesIso_0(A)).hom \\circ (shortComplexH0(A)).f = iCocycles(A,0) \\circ (cochainsIso_0(A)).hom$$$

Lean4

@[reassoc (attr := simp), elementwise (attr := simp)]
theorem cocyclesIso₀_hom_comp_f : (cocyclesIso₀ A).hom ≫ (shortComplexH0 A).f = iCocycles A 0 ≫ (cochainsIso₀ A).hom :=
  by
  dsimp [cocyclesIso₀]
  apply KernelFork.mapOfIsLimit_ι

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