Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Arrow.isoMk

{T : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} T] →
    {P Q W : CategoryTheory.MorphismProperty T} →
      [inst_1 : Q.IsMultiplicative] →
        [inst_2 : W.IsMultiplicative] →
          [Q.RespectsIso] →
            [W.RespectsIso] →
              {A B : P.Arrow Q W} →
                (f : A.left ≅ B.left) →
                  (g : A.right ≅ B.right) →
                    autoParam
                        (CategoryTheory.CategoryStruct.comp f.hom B.hom =
                          CategoryTheory.CategoryStruct.comp A.hom g.hom)
                        CategoryTheory.MorphismProperty.Arrow.isoMk._auto_1 →
                      (A ≅ B)

Make an isomorphism in P.Arrow Q X from isomorphisms in T with compatibilities.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

2 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.MorphismProperty.RespectsIso