Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Arrow.isoMk_hom_left

∀ {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] [inst_3 : Q.RespectsIso] [inst_4 : W.RespectsIso]
  {A B : P.Arrow Q W} (f : A.left ≅ B.left) (g : A.right ≅ B.right)
  (w :
    autoParam (CategoryTheory.CategoryStruct.comp f.hom B.hom = CategoryTheory.CategoryStruct.comp A.hom g.hom)
      CategoryTheory.MorphismProperty.Arrow.isoMk._auto_1),
  (CategoryTheory.MorphismProperty.Arrow.isoMk f g w).hom.left = f.hom

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

0 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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