Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.arrowMap_functor_to_top

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {Φ : CategoryTheory.SmallObject.SuccStruct C}
  {J : Type u} [inst_1 : LinearOrder J] [inst_2 : OrderBot J] [inst_3 : SuccOrder J] [inst_4 : WellFoundedLT J]
  [inst_5 : CategoryTheory.Limits.HasIterationOfShape J C] {j : J} (hj : Order.IsSuccLimit j)
  (iter : (i : J) → i < j → Φ.Iteration i) (i : J) (hi : i < j),
  CategoryTheory.SmallObject.SuccStruct.arrowMap
      (CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.functor hj iter) i j ⋯ ⋯ =
    CategoryTheory.Arrow.mk
      (CategoryTheory.Limits.colimit.ι (CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem iter)
        ⟨i, hi⟩)

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLTCategoryTheory.Limits.HasIterationOfShape