Theorems · Theorem · category theory

CategoryTheory.Quotient.comp_natTransLift_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (r : HomRel C) {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F G H : CategoryTheory.Functor (CategoryTheory.Quotient r) D}
  (τ : (CategoryTheory.Quotient.functor r).comp F ⟶ (CategoryTheory.Quotient.functor r).comp G)
  (τ' : (CategoryTheory.Quotient.functor r).comp G ⟶ (CategoryTheory.Quotient.functor r).comp H)
  {Z : CategoryTheory.Functor (CategoryTheory.Quotient r) D} (h : H ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Quotient.natTransLift r τ)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Quotient.natTransLift r τ') h) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Quotient.natTransLift r (CategoryTheory.CategoryStruct.comp τ τ')) h

Defined in

Mathlib.CategoryTheory.Quotient

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category