Theorems · Inductive type · category theory

CategoryTheory.Localization.Lifting

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {E : Type u_3} →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} E] →
            CategoryTheory.Functor C D →
              CategoryTheory.MorphismProperty C →
                CategoryTheory.Functor C E → CategoryTheory.Functor D E → Type (max u_1 v_3)

When L : C ⥤ D is a localization functor for W : MorphismProperty C and F : C ⥤ E is a functor, we shall say that F' : D ⥤ E lifts F if the obvious diagram is commutative up to an isomorphism.

Defined in

Mathlib.CategoryTheory.Localization.Predicate

Cited by

41 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category