Theorems · Definition · category theory

CategoryTheory.Equivalence.trans

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {E : Type u₃} → [inst_2 : CategoryTheory.Category.{v₃, u₃} E] → (C ≌ D) → (D ≌ E) → (C ≌ E)

Equivalence of categories is transitive.

Defined in

Mathlib.CategoryTheory.Equivalence

Cited by

57 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category