Theorems · Definition · category theory

CategoryTheory.Bicategory.leftZigzagIso

{B : Type u₁} →
  [inst : CategoryTheory.Bicategory B] →
    {a b : B} →
      {f : a ⟶ b} →
        {g : b ⟶ a} →
          (CategoryTheory.CategoryStruct.id a ≅ CategoryTheory.CategoryStruct.comp f g) →
            (CategoryTheory.CategoryStruct.comp g f ≅ CategoryTheory.CategoryStruct.id b) →
              (CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.id a) f ≅
                CategoryTheory.CategoryStruct.comp f (CategoryTheory.CategoryStruct.id b))

The isomorphism version of leftZigzag.

Defined in

Mathlib.CategoryTheory.Bicategory.Adjunction.Basic

Cited by

9 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory