prodComparison_inv_natural_whiskerRight

English

If prodComparison is iso, its inverse is natural in the right argument; i.e., inv(prodComparison F A B) whiskered on the left by f equals whiskered left on F.map f.

Русский

Если prodComparison — изоморфизм, то inv_natural является естественным по правому аргументу; т.е. inv(prodComparison F A B)^{L} = F.map f на левом конце.

LaTeX

$$prodComparison_inv_natural_whiskerLeft F A B f [IsIso (prodComparison F A B')]$$

Lean4

/-- If the product comparison morphism is an iso, its inverse is natural in the left argument. -/
@[reassoc]
theorem prodComparison_inv_natural_whiskerRight (f : A ⟶ A') [IsIso (prodComparison F A' B)] :
    inv (prodComparison F A B) ≫ F.map (f ▷ B) = (F.map f ▷ F.obj B) ≫ inv (prodComparison F A' B) := by
  rw [IsIso.eq_comp_inv, Category.assoc, IsIso.inv_comp_eq, prodComparison_natural_whiskerRight]

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