Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.mapObj_trans

∀ {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 j₃ : J}
  (iter₁ : Φ.Iteration j₁) (iter₂ : Φ.Iteration j₂) (iter₃ : Φ.Iteration j₃) {k₁ k₂ k₃ : J} (h₁₂ : k₁ ≤ k₂)
  (h₂₃ : k₂ ≤ k₃) (h₁ : k₁ ≤ j₁) (h₂ : k₂ ≤ j₂) (h₃ : k₃ ≤ j₃) (h₁₂' : j₁ ≤ j₂) (h₂₃' : j₂ ≤ j₃),
  CategoryTheory.CategoryStruct.comp (iter₁.mapObj iter₂ h₁₂ h₁ h₂ h₁₂') (iter₂.mapObj iter₃ h₂₃ h₂ h₃ h₂₃') =
    iter₁.mapObj iter₃ ⋯ h₁ h₃ ⋯

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Basic

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotCategoryTheory.Limits.HasIterationOfShapeWellFoundedLT