Theorems · Definition · category theory

CategoryTheory.TransfiniteCompositionOfShape.iic

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : Type w} →
      [inst_1 : LinearOrder J] →
        [inst_2 : OrderBot J] →
          {X Y : C} →
            {f : X ⟶ Y} →
              [inst_3 : SuccOrder J] →
                [inst_4 : WellFoundedLT J] →
                  (c : CategoryTheory.TransfiniteCompositionOfShape J f) →
                    (j : J) →
                      CategoryTheory.TransfiniteCompositionOfShape (↑(Set.Iic j)) (c.F.map (CategoryTheory.homOfLE ⋯))

A transfinite composition of shape J induces a transfinite composition of shape Set.Iic j for any j : J.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape

Cited by

3 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLT