Theorems · Definition · category theory

CategoryTheory.LocalizedMonoidal

{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] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          (L : CategoryTheory.Functor C D) →
            (W : CategoryTheory.MorphismProperty C) →
              [W.IsMonoidal] →
                [L.IsLocalization W] →
                  {unit : D} → (L.obj (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) ≅ unit) → Type u_2

Given a monoidal category C, a localization functor L : C ⥤ D with respect to W : MorphismProperty C which satisfies W.IsMonoidal, and a choice of object unit : D with an isomorphism L.obj (𝟙_ C) ≅ unit, this is a type synonym for D on which we define the localized monoidal category structure.

Defined in

Mathlib.CategoryTheory.Localization.Monoidal.Basic

Cited by

55 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MorphismProperty.IsMonoidalCategoryTheory.Functor.IsLocalization