braidingInvCorepresenting — Mathlib

English

The unit of DayConvolution interacts with braiding via a natural equation relating evaluations at tensor products.

Русский

Единица DayConvolution взаимодействует с braiding по естественному равенству на Tensor-продуктах.

LaTeX

$$$\text{unit app braiding hom app}$$$

Lean4

/-- The natural transformation `F ⊠ G ⟶ (tensor C) ⋙ (G ⊛ F)` that corepresents
the braiding morphism `F ⊛ G ⟶ G ⊛ F`. -/
@[simps]
def braidingInvCorepresenting : G ⊠ F ⟶ tensor C ⋙ F ⊛ G
    where
  app _ := (β_ _ _).inv ≫ (unit F G).app (_, _) ≫ (F ⊛ G).map (β_ _ _).inv
  naturality {x y} f := by simp [tensorHom_def, ← Functor.map_comp]

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