Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.arrow_mk_mapObj

∀ {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} (h₁₂ : k₁ ≤ k₂) (h₁ : k₁ ≤ j₁) (h₂ : k₂ ≤ j₂)
  (hj : j₁ ≤ j₂),
  CategoryTheory.Arrow.mk (iter₁.mapObj iter₂ h₁₂ h₁ h₂ hj) =
    CategoryTheory.SmallObject.SuccStruct.arrowMap iter₂.F k₁ k₂ h₁₂ h₂

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