instHasCokernels — Mathlib

English

The category SemiNormedGrp₁ has cokernels.

Русский

Категория SemiNormedGrp₁ имеет кокernel.

LaTeX

$$$\\\\text{HasCokernels}(\\\\text{SemiNormedGrp}_1).$$$

Lean4

instance : HasCokernels SemiNormedGrp₁.{u} where
  has_colimit
    f :=
    HasColimit.mk
      { cocone := cokernelCocone f
        isColimit :=
          isColimitAux _ (cokernelLift f)
            (fun s => by
              ext
              apply NormedAddGroupHom.lift_mk f.1.range
              rintro _ ⟨b, rfl⟩
              change (f ≫ s.π) b = 0
              simp)
            fun _ _ w =>
            SemiNormedGrp₁.hom_ext <|
              Subtype.eq (NormedAddGroupHom.lift_unique f.1.range _ _ _ (congr_arg Subtype.val (congr_arg Hom.hom w))) }
        -- Sanity check

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