Theorems · Definition · category theory

CategoryTheory.Localization.Construction.NatTransExtension.app

{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) → (X : W.Localization) → F₁.obj X ⟶ F₂.obj X

If F₁ and F₂ are functors W.Localization ⥤ D and if we have τ : W.Q ⋙ F₁ ⟶ W.Q ⋙ F₂, we shall define a natural transformation F₁ ⟶ F₂. This is the app field of this natural transformation.

Defined in

Mathlib.CategoryTheory.Localization.Construction

Cited by

3 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category