Theorems · Definition · category theory

CategoryTheory.SmallObject.iterationFunctor

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (I : CategoryTheory.MorphismProperty C) →
      (κ : Cardinal.{w}) →
        [inst_1 : Fact κ.IsRegular] →
          [inst_2 : OrderBot κ.ord.ToType] →
            [I.IsCardinalForSmallObjectArgument κ] →
              CategoryTheory.Functor κ.ord.ToType
                (CategoryTheory.Functor (CategoryTheory.Arrow C) (CategoryTheory.Arrow C))

The functor κ.ord.ToType ⥤ Arrow C ⥤ Arrow C corresponding to the iterations of the successor structure succStruct I κ.

Defined in

Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument

Cited by

10 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFactOrderBotCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument