Theorems · Definition · category theory

CategoryTheory.OrthogonalReflection.iterationObjSuccIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (W : CategoryTheory.MorphismProperty C) →
      (Z : C) →
        [inst_1 : CategoryTheory.Limits.HasPushouts C] →
          [inst_2 : ∀ (Z : C), CategoryTheory.Limits.HasCoproduct CategoryTheory.OrthogonalReflection.D₁.obj₁] →
            [inst_3 : ∀ (Z : C), CategoryTheory.Limits.HasCoproduct CategoryTheory.OrthogonalReflection.D₁.obj₂] →
              [inst_4 :
                  ∀ (Z : C),
                    CategoryTheory.Limits.HasMulticoequalizer
                      (CategoryTheory.OrthogonalReflection.D₂.multispanIndex W Z)] →
                (κ : Cardinal.{w}) →
                  [inst_5 : OrderBot κ.ord.ToType] →
                    [inst_6 : CategoryTheory.Limits.HasIterationOfShape κ.ord.ToType C] →
                      [Fact κ.IsRegular] →
                        (j : κ.ord.ToType) →
                          (CategoryTheory.OrthogonalReflection.iteration W Z κ).obj (Order.succ j) ≅
                            CategoryTheory.OrthogonalReflection.succ W
                              ((CategoryTheory.OrthogonalReflection.iteration W Z κ).obj j)

(iteration W Z κ).obj (Order.succ j) identifies to the image of (iteration W Z κ).obj j by succ.

Defined in

Mathlib.CategoryTheory.Presentable.OrthogonalReflection

Cited by

5 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasCoproductCategoryTheory.Limits.HasCoproductCategoryTheory.Limits.HasMulticoequalizerOrderBotCategoryTheory.Limits.HasIterationOfShapeFact