Theorems · Definition · category theory

CategoryTheory.SmallObject.iterationFunctorObjObjRightIso

{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] →
            [inst_3 : I.IsCardinalForSmallObjectArgument κ] →
              (f : CategoryTheory.Arrow C) →
                (j : κ.ord.ToType) → (((CategoryTheory.SmallObject.iterationFunctor I κ).obj j).obj f).right ≅ f.right

For any f : Arrow C and j : κ.ord.ToType, the object (((iterationFunctor I κ).obj j).obj f).right identifies to f.right.

Defined in

Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument

Cited by

4 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryFactOrderBotCategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument