Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Comma.Hom.comp

{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} →
                      [Q.IsStableUnderComposition] →
                        [W.IsStableUnderComposition] →
                          {X Y Z : CategoryTheory.MorphismProperty.Comma L R P Q W} → X.Hom Y → Y.Hom Z → X.Hom Z

Composition of morphisms in P.Comma L R Q W.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

3 results in Mathlib

Foundations

Depth 10 from the axioms · uses propext, Quot.sound

Assumes

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