Theorems · Theorem · category theory

CategoryTheory.OrthogonalReflection.iteration_map_succ

∀ {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] [inst_7 : Fact κ.IsRegular] (j : κ.ord.ToType),
  (CategoryTheory.OrthogonalReflection.iteration W Z κ).map (CategoryTheory.homOfLE ⋯) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.OrthogonalReflection.toSucc W ((CategoryTheory.OrthogonalReflection.iteration W Z κ).obj j))
      (CategoryTheory.OrthogonalReflection.iterationObjSuccIso W Z κ j).inv

Defined in

Mathlib.CategoryTheory.Presentable.OrthogonalReflection

Cited by

3 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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