case h
β : Type w
C : Type u
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
G : C ⥤ D
f : β → C
inst✝¹ : HasCoproduct f
inst✝ : HasCoproduct fun b => G.obj (f b)
P : C
g : (j : β) → f j ⟶ P
j : β
⊢ Sigma.ι (fun b => G.obj (f b)) j ≫ sigmaComparison G f ≫ G.map (Sigma.desc g) =
    Sigma.ι (fun b => G.obj (f b)) j ≫ Sigma.desc fun j => G.map (g j)
β : Type w
C : Type u
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
G : C ⥤ D
f : β → C
inst✝¹ : HasCoproduct f
inst✝ : HasCoproduct fun b => G.obj (f b)
P : C
g : (j : β) → f j ⟶ P
⊢ sigmaComparison G f ≫ G.map (Sigma.desc g) = Sigma.desc fun j => G.map (g j)
ext j
no goals
case h
β : Type w
C : Type u
inst✝³ : Category C
D : Type u₂
inst✝² : Category D
G : C ⥤ D
f : β → C
inst✝¹ : HasCoproduct f
inst✝ : HasCoproduct fun b => G.obj (f b)
P : C
g : (j : β) → f j ⟶ P
j : β
⊢ Sigma.ι (fun b => G.obj (f b)) j ≫ sigmaComparison G f ≫ G.map (Sigma.desc g) =
    Sigma.ι (fun b => G.obj (f b)) j ≫ Sigma.desc fun j => G.map (g j)
simp only [Discrete.functor_obj, ι_comp_sigmaComparison_assoc, ← G.map_comp, colimit.ι_desc,
  Cofan.mk_pt, Cofan.mk_ι_app]