isStableUnderComposition — Mathlib

English

Given functors F1, F2 and a naturality witness app, the naturality property is stable under composition.

Русский

Для炮 F1, F2 и натурального свидетельства app свойство естественности стабильно под композицию.

LaTeX

$$$(naturalityProperty app).IsStableUnderComposition$$

Lean4

instance isStableUnderComposition {F₁ F₂ : C ⥤ D} (app : ∀ X, F₁.obj X ⟶ F₂.obj X) :
    (naturalityProperty app).IsStableUnderComposition where
  comp_mem f g hf
    hg := by
    simp only [naturalityProperty] at hf hg ⊢
    simp only [Functor.map_comp, Category.assoc, hg]
    slice_lhs 1 2 => rw [hf]
    rw [Category.assoc]

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