Theorems · Definition · category theory

CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso

{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 →
                    {X' Y' : C} →
                      {f' : X' ⟶ Y'} →
                        (CategoryTheory.Arrow.mk f ≅ CategoryTheory.Arrow.mk f') →
                          CategoryTheory.TransfiniteCompositionOfShape J f'

If f and f' are two isomorphic morphisms, and f is a transfinite composition of shape J, then f' also is.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Preorder.TransfiniteCompositionOfShape

Cited by

4 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryLinearOrderOrderBotSuccOrderWellFoundedLT