Theorems · Definition · category theory

CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.functor

{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} →
                    Order.IsSuccLimit j → ((i : J) → i < j → Φ.Iteration i) → CategoryTheory.Functor (↑(Set.Iic j)) C

The extension of inductiveSystem iter to a functor Set.Iic j ⥤ C which sends the top element to the colimit of inductiveSystem iter.

Defined in

Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty

Cited by

3 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLTCategoryTheory.Limits.HasIterationOfShape