dArrowIso₀₁ — Mathlib

English

Equality of the Mk0 image under Theorem cocyclesMk with the IsMul structure.

Русский

Равенство изображений Mk0 в рамках теоремы cocyclesMk с структурой IsMul.

LaTeX

$$$cocyclesMk((cochainsIso_0 A)^{-1} x) = (cocyclesIso_0 A)^{-1} x$$$

Lean4

/-- The arrow `A --d₀₁--> Fun(G, A)` is isomorphic to the differential
`(inhomogeneousCochains A).d 0 1` of the complex of inhomogeneous cochains of `A`. -/
@[simps! hom_left hom_right inv_left inv_right]
def dArrowIso₀₁ : Arrow.mk ((inhomogeneousCochains A).d 0 1) ≅ Arrow.mk (d₀₁ A) :=
  Arrow.isoMk (cochainsIso₀ A) (cochainsIso₁ A) (comp_d₀₁_eq A)

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