Theorems · Definition · category theory

CategoryTheory.Bicategory.eqToHomTransIso

{B : Type u} →
  [inst : CategoryTheory.Bicategory B] →
    {x y z : B} →
      (e₁ : x = y) →
        (e₂ : y = z) →
          CategoryTheory.eqToHom ⋯ ≅
            CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom e₁) (CategoryTheory.eqToHom e₂)

In a bicategory, eqToHoms do not compose strictly, but they do up to isomorphism.

Defined in

Mathlib.CategoryTheory.Bicategory.EqToHom

Cited by

7 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Bicategory