sheafComposeIso_inv_fac — Mathlib

English

The inverse factorization holds: whiskerRight (toSheafify J P) F ≈ toSheafify J (P ⋙ F).

Русский

Обратный факторизационный член: whiskerRight(toSheafify J P) F приблизительно равно toSheafify J (P ⋙ F).

LaTeX

$$$ whiskerRight (toSheafify J P) F \; ≫ (sheafifyComposeIso J F P).inv = toSheafify J (P \⋙ F) $$$

Lean4

@[reassoc (attr := simp)]
theorem sheafComposeIso_inv_fac :
    whiskerRight (toSheafify J P) F ≫ (sheafifyComposeIso J F P).inv = toSheafify J (P ⋙ F) := by
  rw [← sheafComposeIso_hom_fac, assoc, Iso.hom_inv_id, comp_id]

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