Theorems · Definition · category theory

CategoryTheory.LocalizerMorphism.localizedFunctor

{C₁ : Type u₁} →
  {C₂ : Type u₂} →
    {D₁ : Type u₄} →
      {D₂ : Type u₅} →
        [inst : CategoryTheory.Category.{v₁, u₁} C₁] →
          [inst_1 : CategoryTheory.Category.{v₂, u₂} C₂] →
            [inst_2 : CategoryTheory.Category.{v₄, u₄} D₁] →
              [inst_3 : CategoryTheory.Category.{v₅, u₅} D₂] →
                {W₁ : CategoryTheory.MorphismProperty C₁} →
                  {W₂ : CategoryTheory.MorphismProperty C₂} →
                    CategoryTheory.LocalizerMorphism W₁ W₂ →
                      (L₁ : CategoryTheory.Functor C₁ D₁) →
                        [L₁.IsLocalization W₁] →
                          (L₂ : CategoryTheory.Functor C₂ D₂) → [L₂.IsLocalization W₂] → CategoryTheory.Functor D₁ D₂

When Φ : LocalizerMorphism W₁ W₂ and that L₁ and L₂ are localization functors for W₁ and W₂, then Φ.localizedFunctor L₁ L₂ is the induced functor on the localized categories.

Defined in

Mathlib.CategoryTheory.Localization.LocalizerMorphism

Cited by

29 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.IsLocalization