Theorems · Definition · category theory

CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofOrderIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {W : CategoryTheory.MorphismProperty C} →
      {J : Type w} →
        [inst_1 : LinearOrder J] →
          [inst_2 : SuccOrder J] →
            [inst_3 : OrderBot J] →
              [inst_4 : WellFoundedLT J] →
                {X Y : C} →
                  {f : X ⟶ Y} →
                    W.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 → W.TransfiniteCompositionOfShape J' f

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

Defined in

Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderSuccOrderOrderBotWellFoundedLTLinearOrderOrderBotSuccOrderWellFoundedLT