Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot

∀ {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),
  self.F.obj ⟨⊥, ⋯⟩ = Φ.X₀

The zeroth iteration is the zeroth object .

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Basic

Cited by

0 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotCategoryTheory.Limits.HasIterationOfShapeWellFoundedLT