whiskerLeft_leftToRight — Mathlib

English

RightToLeft equals a composition involving left/unitor inverses, whiskers of units, associator inverses, and counits with F.

Русский

RightToLeft равен композиции, включающей обратные унитор/единицы, whisker-операции единиц, обратный ассоциатор и каутинты с F.

LaTeX

$$$t.rightToLeft = H.rightUnitor.inv \circ inv (whiskerLeft H t.adj_1.counit) \circ (Functor.associator _ _ _).inv \circ whiskerRight t.adj_2.counit F \circ F.leftUnitor.hom$$$

Lean4

/-- For an adjoint triple `F ⊣ G ⊣ H` where `F` and `H` are fully faithful, whiskering `G` with the
natural transformation `F ⟶ H` yields the composition of the counit of the first adjunction with
the unit of the second adjunction. -/
@[simp, reassoc]
theorem whiskerLeft_leftToRight : whiskerLeft G t.leftToRight = t.adj₁.counit ≫ t.adj₂.unit := by ext X;
  exact t.leftToRight_app_obj

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