leftOpWhiskerRight — Mathlib

English

The left_op of whiskering on the right respects the left_op structure: leftOp( H.whiskerLeft α ) equals a specified composite with leftOp components.

Русский

Левый Opp برابر whiskerLeft сохраняет структуру leftOp: leftOp( H.whiskerLeft α ) = композиция

LaTeX

$$$\\\\forall {E : Type*} [Category E] {H : E ⥤ C} (α : F ⟶ G) : \\\\mathrm{NatIso}.leftOp( H.whiskerLeft α ) = \\\\mathrm{Functor}.leftOpComp H G .hom \\\\circ whiskerLeft H.leftOp \\\\circ (\\\\mathrm{Functor}.leftOpComp H F).inv.$$$

Lean4

@[reassoc]
theorem leftOpWhiskerRight {E : Type*} [Category E] {H : E ⥤ C} (α : F ⟶ G) :
    (whiskerLeft H α).leftOp = (Functor.leftOpComp H G).hom ≫ whiskerLeft _ α.leftOp ≫ (Functor.leftOpComp H F).inv :=
  by cat_disch

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