braidingHomCorepresenting — Mathlib

English

Auxiliary proof confirming the associativity condition in the monoid structure on Day convolution.

Русский

Вспомогательное доказательство ассоциативности в структуре моноида DayConvolution.

LaTeX

$$$\text{(npowRecAuto)}(0, x) = \text{npowRecAuto}(0, x)$$$

Lean4

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

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