C : Type u_2
inst✝¹ : Category C
inst✝ : HasFiniteCoproducts C
X Y : SimplicialObject C
s : Splitting X
n : ℕ
⊢ ι s (len (IndexSet.id [n].op).fst.unop) = ι s n
C : Type u_2
inst✝¹ : Category C
inst✝ : HasFiniteCoproducts C
X Y : SimplicialObject C
s : Splitting X
n : ℕ
⊢ ιSummand s (IndexSet.id [n].op) = ι s n
erw [ιSummand_eq, X.map_id, comp_id]
no goals
C : Type u_2
inst✝¹ : Category C
inst✝ : HasFiniteCoproducts C
X Y : SimplicialObject C
s : Splitting X
n : ℕ
⊢ ι s (len (IndexSet.id [n].op).fst.unop) = ι s n
rfl