Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Comma.isoMk

{A : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} A] →
    {B : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} B] →
        {T : Type u_3} →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} T] →
            {L : CategoryTheory.Functor A T} →
              {R : CategoryTheory.Functor B T} →
                {P : CategoryTheory.MorphismProperty T} →
                  {Q : CategoryTheory.MorphismProperty A} →
                    {W : CategoryTheory.MorphismProperty B} →
                      [inst_3 : Q.IsMultiplicative] →
                        [inst_4 : W.IsMultiplicative] →
                          [Q.RespectsIso] →
                            [W.RespectsIso] →
                              {X Y : CategoryTheory.MorphismProperty.Comma L R P Q W} →
                                (l : X.left ≅ Y.left) →
                                  (r : X.right ≅ Y.right) →
                                    autoParam
                                        (CategoryTheory.CategoryStruct.comp (L.map l.hom) Y.hom =
                                          CategoryTheory.CategoryStruct.comp X.hom (R.map r.hom))
                                        CategoryTheory.MorphismProperty.Comma.isoMk._auto_1 →
                                      (X ≅ Y)

Constructor for isomorphisms in P.Comma L R Q W from isomorphisms of the left and right components and naturality in the forward direction.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

5 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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