prodComparisonNatTrans — Mathlib

English

A simplified invariant form of the fst map under inverse prodComparison arising from isomorphism assumptions.

Русский

Упрощенная форма инвариантности fst под обратным prodComparison при предположении изоморфизма.

LaTeX

$$inv_prodComparison_map_fst_simp F A B$$

Lean4

/-- The product comparison morphism from `F(A ⊗ -)` to `FA ⊗ F-`, whose components are given by
`prodComparison`. -/
@[simps]
def prodComparisonNatTrans (A : C) : (curriedTensor C).obj A ⋙ F ⟶ F ⋙ (curriedTensor D).obj (F.obj A)
    where
  app B := prodComparison F A B
  naturality x y
    f := by
    apply hom_ext <;>
      simp only [Functor.comp_obj, curriedTensor_obj_obj, Functor.comp_map, curriedTensor_obj_map, Category.assoc,
        prodComparison_fst, whiskerLeft_fst, prodComparison_snd, prodComparison_snd_assoc, whiskerLeft_snd,
        ← F.map_comp]

Похожие утверждения