Theorems · Definition · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.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} →
                          k₁ ≤ k₂ →
                            (h₁ : k₁ ≤ j₁) → (h₂ : k₂ ≤ j₂) → j₁ ≤ j₂ → (iter₁.F.obj ⟨k₁, h₁⟩ ⟶ iter₂.F.obj ⟨k₂, h₂⟩)

Given iter₁ : Φ.Iteration j₁ and iter₂ : Φ.Iteration j₂, with j₁ ≤ j₂, if k₁ ≤ k₂ are elements such that k₁ ≤ j₁ and k₂ ≤ k₂, then this is the canonical map iter₁.F.obj ⟨k₁, h₁⟩ ⟶ iter₂.F.obj ⟨k₂, h₂⟩.

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Basic

Cited by

7 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotCategoryTheory.Limits.HasIterationOfShapeWellFoundedLT