Theorems · Theorem · category theory

CategoryTheory.Lax.LaxTrans.isoMk_inv_as_app

∀ {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.whiskerRight (app a).hom (G.map f))
            (θ.naturality f) =
          CategoryTheory.CategoryStruct.comp (η.naturality f)
            (CategoryTheory.Bicategory.whiskerLeft (F.map f) (app b).hom))
      CategoryTheory.Lax.LaxTrans.isoMk._auto_1)
  (a : B), (CategoryTheory.Lax.LaxTrans.isoMk app naturality).inv.as.app a = (app a).inv

Defined in

Mathlib.CategoryTheory.Bicategory.Modification.Lax

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.BicategoryCategoryTheory.Bicategory