proposition: Lemma path_morphism abf a'b'f' (gh g'h' : morphism abf a'b'f') : gh.(g) = g'h'.(g) -> gh.(h) = g'h'.(h) -> gh = g'h'.
proof: Proof. destruct gh, g'h'; simpl. intros; path_induction. f_ap. all:exact (center _). Qed.
imports: Functor.Core InitialTerminalCategory.Core InitialTerminalCategory.Functors Category.Strict HoTT.Basics HoTT.Types