Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.iterationFunctor_map_succ_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (Φ : CategoryTheory.SmallObject.SuccStruct C) {J : Type w}
  [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 : ¬IsMax j) {Z : C}
  (h : (Φ.iterationFunctor J).obj (Order.succ j) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((Φ.iterationFunctor J).map (CategoryTheory.homOfLE ⋯)) h =
    CategoryTheory.CategoryStruct.comp (Φ.toSucc ((Φ.iterationFunctor J).obj j))
      (CategoryTheory.CategoryStruct.comp (Φ.iterationFunctorObjSuccIso j hj).inv h)

Defined in

Mathlib.CategoryTheory.SmallObject.TransfiniteIteration

Cited by

0 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLTCategoryTheory.Limits.HasIterationOfShape