Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.arrowSucc_eq

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : Type w} {Φ : CategoryTheory.SmallObject.SuccStruct C}
  [inst_1 : LinearOrder J] [inst_2 : SuccOrder J] [inst_3 : OrderBot J]
  [inst_4 : CategoryTheory.Limits.HasIterationOfShape J C] [inst_5 : WellFoundedLT J] {j : J} (self : Φ.Iteration j)
  (i : J) (hi : i < j), CategoryTheory.SmallObject.SuccStruct.arrowSucc self.F i hi = Φ.toSuccArrow (self.F.obj ⟨i, ⋯⟩)

The iteration on a successor element is the successor.

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Basic

Cited by

2 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotCategoryTheory.Limits.HasIterationOfShapeWellFoundedLT