Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.congr_map

∀ {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] {j₁ j₂ : J}
  (iter₁ : Φ.Iteration j₁) (iter₂ : Φ.Iteration j₂) {k₁ k₂ : J} (h : k₁ ≤ k₂) (h₁ : k₂ ≤ j₁) (h₂ : k₂ ≤ j₂),
  iter₁.F.map (CategoryTheory.homOfLE h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯)
      (CategoryTheory.CategoryStruct.comp (iter₂.F.map (CategoryTheory.homOfLE h)) (CategoryTheory.eqToHom ⋯))

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Basic

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotCategoryTheory.Limits.HasIterationOfShapeWellFoundedLT