Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.Comma.Hom.comp_left

∀ {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.IsStableUnderComposition]
  [inst_4 : W.IsStableUnderComposition] {X Y Z : CategoryTheory.MorphismProperty.Comma L R P Q W} (f : X.Hom Y)
  (g : Y.Hom Z), (f.comp g).left = CategoryTheory.CategoryStruct.comp f.left g.left

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

0 results in Mathlib

Foundations

Depth 11 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsStableUnderComposition