Theorems · Theorem · category theory

CategoryTheory.OrthogonalReflection.isLocal_isLocal_reflection

∀ {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],
  W.isLocal.isLocal (CategoryTheory.OrthogonalReflection.reflection W Z κ)

Defined in

Mathlib.CategoryTheory.Presentable.OrthogonalReflection

Cited by

0 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasCoproductCategoryTheory.Limits.HasCoproductCategoryTheory.Limits.HasMulticoequalizerOrderBotCategoryTheory.Limits.HasIterationOfShape