selRightfAction — Mathlib

English

Right-action morphisms respect composition in D: actionHomRight w (f ≫ g) = actionHomRight w f ≫ actionHomRight w g.

Русский

Правые отображения действия уважают композицию в D: actionHomRight w (f ∘ g) = actionHomRight w f ∘ actionHomRight w g.

LaTeX

$$actionHomRight_comp$$

Lean4

/-- A monoidal category acts on itself through the tensor product. -/
@[simps!]
instance selRightfAction [MonoidalCategory C] : MonoidalRightAction C C
    where
  actionObj x y := x ⊗ y
  actionHom f g := f ⊗ₘ g
  actionUnitIso x := ρ_ x
  actionAssocIso x y z := α_ x y z |>.symm
  actionHomLeft f x := f ▷ x
  actionHomRight x _ _ f := x ◁ f
  actionHom_def := by simp [tensorHom_def]

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