Theorems · Definition · category theory

CategoryTheory.Quotient.natIsoLift

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    (r : HomRel C) →
      {D : Type u_2} →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
          {F G : CategoryTheory.Functor (CategoryTheory.Quotient r) D} →
            ((CategoryTheory.Quotient.functor r).comp F ≅ (CategoryTheory.Quotient.functor r).comp G) → (F ≅ G)

In order to define a natural isomorphism F ≅ G with F G : Quotient r ⥤ D, it suffices to do so after precomposing with Quotient.functor r.

Defined in

Mathlib.CategoryTheory.Quotient

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category