Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Under.isoMk

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

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

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

4 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIso