Theorems · Definition · category theory

CategoryTheory.Localization.Construction.natTransExtension

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {D : Type uD} →
        [inst_1 : CategoryTheory.Category.{uD', uD} D] →
          {F₁ F₂ : CategoryTheory.Functor W.Localization D} → (W.Q.comp F₁ ⟶ W.Q.comp F₂) → (F₁ ⟶ F₂)

If F₁ and F₂ are functors W.Localization ⥤ D, a natural transformation F₁ ⟶ F₂ can be obtained from a natural transformation W.Q ⋙ F₁ ⟶ W.Q ⋙ F₂.

Defined in

Mathlib.CategoryTheory.Localization.Construction

Cited by

3 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category