Theorems · Theorem · category theory

CategoryTheory.Join.mapPairComp_hom_app_right

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {E : Type u₃} [inst_2 : CategoryTheory.Category.{v₃, u₃} E] {E' : Type u₄}
  [inst_3 : CategoryTheory.Category.{v₄, u₄} E'] {J : Type u₅} [inst_4 : CategoryTheory.Category.{v₅, u₅} J]
  {K : Type u₆} [inst_5 : CategoryTheory.Category.{v₆, u₆} K] (Fₗ : CategoryTheory.Functor C E)
  (Fᵣ : CategoryTheory.Functor D E') (Gₗ : CategoryTheory.Functor E J) (Gᵣ : CategoryTheory.Functor E' K) (d : D),
  (CategoryTheory.Join.mapPairComp Fₗ Fᵣ Gₗ Gᵣ).hom.app (CategoryTheory.Join.right d) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Join.right (Gᵣ.obj (Fᵣ.obj d)))

Defined in

Mathlib.CategoryTheory.Join.Basic

Cited by

10 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category