Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Comma.id_hom

∀ {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] (X : CategoryTheory.MorphismProperty.Comma L R P Q W),
  CategoryTheory.MorphismProperty.Comma.Hom.hom (CategoryTheory.CategoryStruct.id X) =
    CategoryTheory.CategoryStruct.id X.toComma

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

1 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsMultiplicative