Theorems · Theorem · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.mk.sizeOf_spec

∀ {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] {j : J} [inst_6 : SizeOf C]
  [inst_7 : SizeOf J] (F : CategoryTheory.Functor (↑(Set.Iic j)) C) (obj_bot : F.obj ⟨⊥, ⋯⟩ = Φ.X₀)
  (arrowSucc_eq :
    ∀ (i : J) (hi : i < j), CategoryTheory.SmallObject.SuccStruct.arrowSucc F i hi = Φ.toSuccArrow (F.obj ⟨i, ⋯⟩))
  (arrowMap_limit :
    ∀ (i : J) (hi : Order.IsSuccLimit i) (hij : i ≤ j) (k : J) (hk : k < i),
      CategoryTheory.SmallObject.SuccStruct.arrowMap F k i ⋯ hij =
        CategoryTheory.SmallObject.SuccStruct.arrowι (CategoryTheory.SmallObject.restrictionLT F hij) hi k hk),
  sizeOf { F := F, obj_bot := obj_bot, arrowSucc_eq := arrowSucc_eq, arrowMap_limit := arrowMap_limit } =
    1 + sizeOf F + sizeOf obj_bot

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Basic

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotCategoryTheory.Limits.HasIterationOfShapeWellFoundedLTSizeOfSizeOf