Lemma from_matrix_entry {C:category} {I} {d:I -> ob C} (D:Product d) {J} {b:J -> ob C} (B:Sum b) (f : ∏ i j, Hom C (b j) (d i)) : ∏ i j, (universalElement D i ∘ from_matrix D B f) ∘ opp_mor (universalElement B j) = f i j. Proof. intros. exact (eqtohomot (eqtohomot (homotweqinvweq (to_matrix D B) f) i) j). Qed.
Require Import