Theorems · Theorem · category theory

CategoryTheory.Lax.OplaxTrans.Modification.mk.injEq

∀ {B : Type u₁} [inst : CategoryTheory.Bicategory B] {C : Type u₂} [inst_1 : CategoryTheory.Bicategory C]
  {F G : CategoryTheory.LaxFunctor B C} {η θ : F ⟶ G} (app : (a : B) → η.app a ⟶ θ.app a)
  (naturality :
    autoParam
      (∀ {a b : B} (f : a ⟶ b),
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (app b)) (θ.naturality f) =
          CategoryTheory.CategoryStruct.comp (η.naturality f)
            (CategoryTheory.Bicategory.whiskerRight (app a) (G.map f)))
      CategoryTheory.Lax.OplaxTrans.Modification.naturality._autoParam)
  (app_1 : (a : B) → η.app a ⟶ θ.app a)
  (naturality_1 :
    autoParam
      (∀ {a b : B} (f : a ⟶ b),
        CategoryTheory.CategoryStruct.comp (CategoryTheory.Bicategory.whiskerLeft (F.map f) (app_1 b))
            (θ.naturality f) =
          CategoryTheory.CategoryStruct.comp (η.naturality f)
            (CategoryTheory.Bicategory.whiskerRight (app_1 a) (G.map f)))
      CategoryTheory.Lax.OplaxTrans.Modification.naturality._autoParam),
  ({ app := app, naturality := naturality } = { app := app_1, naturality := naturality_1 }) = (app = app_1)

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Lax

Cited by

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Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory