Theorems · Theorem · category theory

CategoryTheory.Bicategory.pentagon_inv

∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {a b c d e : B} (f : a ⟶ b) (g : b ⟶ c) (h : c ⟶ d) (i : d ⟶ e),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.whiskerLeft f (CategoryTheory.Bicategory.associator g h i).inv)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Bicategory.associator f (CategoryTheory.CategoryStruct.comp g h) i).inv
        (CategoryTheory.Bicategory.whiskerRight (CategoryTheory.Bicategory.associator f g h).inv i)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Bicategory.associator f g (CategoryTheory.CategoryStruct.comp h i)).inv
      (CategoryTheory.Bicategory.associator (CategoryTheory.CategoryStruct.comp f g) h i).inv

Defined in

Mathlib.CategoryTheory.Bicategory.Basic

Cited by

3 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory