Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Comma.mapRightEq_hom_app_right

∀ {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) {P : CategoryTheory.MorphismProperty T} {Q : CategoryTheory.MorphismProperty A}
  {W : CategoryTheory.MorphismProperty B} [inst_3 : Q.IsMultiplicative] [inst_4 : W.IsMultiplicative]
  {R₁ R₂ : CategoryTheory.Functor B T} [inst_5 : Q.RespectsIso] [inst_6 : W.RespectsIso] (r r' : R₁ ⟶ R₂) (h : r = r')
  (hr :
    ∀ (X : CategoryTheory.MorphismProperty.Comma L R₁ P Q W),
      P (CategoryTheory.CategoryStruct.comp X.hom (r.app X.right)))
  (X : CategoryTheory.MorphismProperty.Comma L R₁ P Q W),
  ((CategoryTheory.MorphismProperty.Comma.mapRightEq L r r' h hr).hom.app X).right =
    CategoryTheory.CategoryStruct.id X.right

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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