Theorems · Definition · category theory

CategoryTheory.SmallObject.SuccStruct.iterationFunctorObjBotIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (Φ : CategoryTheory.SmallObject.SuccStruct C) →
      (J : Type w) →
        [inst_1 : LinearOrder J] →
          [inst_2 : OrderBot J] →
            [inst_3 : SuccOrder J] →
              [inst_4 : WellFoundedLT J] →
                [inst_5 : CategoryTheory.Limits.HasIterationOfShape J C] → (Φ.iterationFunctor J).obj ⊥ ≅ Φ.X₀

The isomorphism (Φ.iterationFunctor J).obj ⊥ ≅ Φ.X₀.

Defined in

Mathlib.CategoryTheory.SmallObject.TransfiniteIteration

Cited by

1 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLTCategoryTheory.Limits.HasIterationOfShape