coequalizerCofork — Mathlib

English

For every point x in a LocallyRingedSpace X, the residue field κ(x) is a field.

Русский

Для каждой точки x пространства LocallyRingedSpace X остаточное поле κ(x) является полем.

LaTeX

$$Field( X.residueField x )$$

Lean4

/-- The explicit coequalizer cofork of locally ringed spaces. -/
noncomputable def coequalizerCofork : Cofork f g :=
  @Cofork.ofπ _ _ _ _ f g (coequalizer f g)
    ⟨coequalizer.π f.toShHom g.toShHom,
      -- Porting note: this used to be automatic
      HasCoequalizer.coequalizer_π_stalk_isLocalHom _ _⟩
    (LocallyRingedSpace.Hom.ext' (coequalizer.condition f.toShHom g.toShHom))

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