explicitCokernelIso_hom_desc — Mathlib

English

The hom component of the explicit cokernel iso, followed by cokernel.desc, recovers the explicitCokernelDesc from w.

Русский

Гом-часть явного кокernel-изоморфизма, затем cokernel.desc, восстанавливает явноеCokernelDesc из w.

LaTeX

$$$ (explicitCokernelIso f).hom \circ cokernel.desc f g w = explicitCokernelDesc w $$$

Lean4

@[simp]
theorem explicitCokernelIso_hom_desc {X Y Z : SemiNormedGrp.{u}} {f : X ⟶ Y} {g : Y ⟶ Z} (w : f ≫ g = 0) :
    (explicitCokernelIso f).hom ≫ cokernel.desc f g w = explicitCokernelDesc w :=
  by
  ext1
  simp [explicitCokernelDesc, explicitCokernelπ, explicitCokernelIso, IsColimit.coconePointUniqueUpToIso]

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