Theorems · Definition · category theory

CategoryTheory.SmallObject.SuccStruct.iter

{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] → (j : J) → Φ.Iteration j

Given Φ : SuccStruct C and an element j : J in a well-ordered type, this is the unique element in Φ.Iteration j.

Defined in

Mathlib.CategoryTheory.SmallObject.TransfiniteIteration

Cited by

2 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLTCategoryTheory.Limits.HasIterationOfShape