Theorems · Definition · category theory

CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso

{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] →
                  CategoryTheory.TransfiniteCompositionOfShape J f →
                    {J' : Type w'} →
                      [inst_5 : LinearOrder J'] →
                        [inst_6 : OrderBot J'] →
                          [inst_7 : SuccOrder J'] →
                            [inst_8 : WellFoundedLT J'] → J' ≃o J → CategoryTheory.TransfiniteCompositionOfShape J' f

If f is a transfinite composition of shape J, then it is also a transfinite composition of shape J' if J' ≃o J.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape

Cited by

3 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLTLinearOrderOrderBotSuccOrderWellFoundedLT