whiskerLeft_natTransExtension — Mathlib

English

For W.Q, the whiskering with W.Q of the natural transformation extension τ equals τ itself: whiskerLeft W.Q (natTransExtension τ) = τ.

Русский

Для W.Q картина натрансформирования: обрамление whiskerLeft W.Q (natTransExtension τ) равно τ.

LaTeX

$$$\operatorname{whiskerLeft}(W.Q, \operatorname{natTransExtension}(\tau)) = \tau$$$

Lean4

@[simp]
theorem whiskerLeft_natTransExtension {F G : W.Localization ⥤ D} (τ : W.Q ⋙ F ⟶ W.Q ⋙ G) :
    whiskerLeft W.Q (natTransExtension τ) = τ := by
  cat_disch
    -- This is not a simp lemma, because the simp norm form of the left-hand side uses `whiskerLeft`.

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