English
Two natural transformations between quotient-functor compositions compose via natTransLift to equal the natTransLift of their component composition.
Русский
Две натурП преобразования между композициями функторов Quotient образуют равенство через natTransLift от композиции трансформаций.
LaTeX
$$$\forall {F G H : Quotient(r) \to D}$, $τ : Quotient.functor r \circ F \Rightarrow Quotient.functor r \circ G$, $τ' : Quotient.functor r \circ G \Rightarrow Quotient.functor r \circ H$, \\n$ natTransLift r τ \;\circ\; natTransLift r τ' = natTransLift r (τ \circ τ').$$$
Lean4
@[reassoc]
theorem comp_natTransLift {F G H : Quotient r ⥤ D} (τ : Quotient.functor r ⋙ F ⟶ Quotient.functor r ⋙ G)
(τ' : Quotient.functor r ⋙ G ⟶ Quotient.functor r ⋙ H) :
natTransLift r τ ≫ natTransLift r τ' = natTransLift r (τ ≫ τ') := by cat_disch
