rightDerivedNatTrans_fac — Mathlib

English

The rightDerivedNatTrans is natural in τ and respects composition with α and α' under localization.

Русский

ПравыйDerivedNatTrans естественно по τ и сохраняет композицию с α и α' при локализации.

LaTeX

$$[τ : F ⟶ F'] : α.app X ≫ (rightDerivedNatTrans RF RF' α α' W τ).app (L.obj X) = τ.app X ≫ α'.app X$$

Lean4

@[reassoc (attr := simp)]
theorem rightDerivedNatTrans_fac (τ : F ⟶ F') : α ≫ whiskerLeft L (rightDerivedNatTrans RF RF' α α' W τ) = τ ≫ α' :=
  by
  dsimp only [rightDerivedNatTrans]
  simp

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